id int32 1 6.98k | cdls dict | question_en stringlengths 58 424 | question_cn stringlengths 20 201 | answer stringclasses 906
values | image imagewidth (px) 48 1.6k | code stringlengths 988 2.44k |
|---|---|---|---|---|---|---|
1 | {
"construction_cdl": [
"Shape(RS,ST,TR)",
"Shape(XY,YZ,ZX)"
],
"text_cdl": [
"CongruentBetweenTriangle(RST,XYZ)",
"Equal(LengthOfLine(TR),x+21)",
"Equal(LengthOfLine(ZX),2*x-14)",
"Equal(MeasureOfAngle(TRS),4*y-10)",
"Equal(MeasureOfAngle(ZXY),3*y+5)"
],
"image_cdl": [
"Equal(LengthOfLine(TR),x+21)",
"Equal(LengthOfLine(ZX),2*x-14)",
"Equal(MeasureOfAngle(TRS),4*y-10)",
"Equal(MeasureOfAngle(ZXY),3*y+5)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, triangle RST is congruent to triangle XYZ, TR=x+21, ZX=2*x-14, ∠TRS=4*y-10°, ∠ZXY=3*y+5°. Find the value of y. | 如图所示，三角形RST与三角形XYZ是全等三角形，TR=x+21，ZX=2*x-14，∠TRS=4*y-10°，∠ZXY=3*y+5°。求y的值。 | 15 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [0.5000000000000001, 0.8660254037844386], "T": [-0.4999999999999998, 0.8660254037844387], "X": [-1.0, 1.2246467991473532e-16], "Y": [-0.5000000000000004, -0.8660254037844384], "Z": [0.5000000000000001, -0.8660254037844386]}
shapes = [["R", "S", "S", "T", "T", "R"], ["X", "Y", "Y", "Z", "Z", "X"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 1')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
2 | {
"construction_cdl": [
"Shape(MR,RQ,QM)",
"Shape(QR,RP,PQ)",
"Shape(MQ,QN,NM)",
"Shape(QP,PN,NQ)",
"Collinear(MQP)",
"Collinear(RQN)"
],
"text_cdl": [
"Equal(LengthOfLine(MN),3*x-4)",
"Equal(LengthOfLine(NQ),15)",
"Equal(LengthOfLine(PN),2*y+5)",
"Equal(LengthOfLine(PQ),12)",
"Equal(LengthOfLine(RM),18)",
"Equal(LengthOfLine(RP),20)",
"Equal(LengthOfLine(RQ),3*z-3)",
"Equal(MeasureOfAngle(MRQ),38)",
"Equal(MeasureOfAngle(NQP),83)",
"Equal(MeasureOfAngle(QNM),33)",
"Parallelogram(MRPN)"
],
"image_cdl": [
"Equal(LengthOfLine(MN),3*x-4)",
"Equal(LengthOfLine(NQ),15)",
"Equal(LengthOfLine(PN),2*y+5)",
"Equal(LengthOfLine(PQ),12)",
"Equal(LengthOfLine(RM),18)",
"Equal(LengthOfLine(RP),20)",
"Equal(LengthOfLine(RQ),3*z-3)",
"Equal(MeasureOfAngle(MRQ),38)",
"Equal(MeasureOfAngle(NQP),83)",
"Equal(MeasureOfAngle(QNM),33)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, MN=3*x-4, NQ=15, PN=2*y+5, PQ=12, RM=18, RP=20, RQ=3*z-3, ∠MRQ=38°, ∠NQP=83°, ∠QNM=33°, MN and RP are opposite sides of the ▱ MRPN. Find the value of y. | 如图所示，MN=3*x-4，NQ=15，PN=2*y+5，PQ=12，RM=18，RP=20，RQ=3*z-3，∠MRQ=38°，∠NQP=83°，∠QNM=33°，RM和PN是▱MRPN的一组对边。求y的值。 | 13/2 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.30901699437494723, -0.9510565162951536], "S": [0.5000000000000001, 0.8660254037844386], "T": [-0.4999999999999998, 0.8660254037844387], "X": [-1.0, 1.2246467991473532e-16], "Y": [-0.5000000000000004, -0.8660254037844384], "Z": [0.5000000000000001, -0.8660254037844386], "M": [1.0, 0.0], "N": [0.30901699437494745, 0.9510565162951535], "P": [-0.8090169943749473, 0.5877852522924732], "Q": [-0.8090169943749476, -0.587785252292473]}
shapes = [["M", "R", "R", "Q", "Q", "M"], ["Q", "R", "R", "P", "P", "Q"], ["M", "Q", "Q", "N", "N", "M"], ["Q", "P", "P", "N", "N", "Q"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 2')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
3 | {
"construction_cdl": [
"Shape(RA,AB,BS,SR)",
"Shape(AJ,JK,KB,BA)",
"Shape(JQ,QT,TK,KJ)",
"Collinear(RAJQ)",
"Collinear(SBKT)"
],
"text_cdl": [
"Equal(LengthOfLine(BT),LengthOfLine(SB))",
"Equal(LengthOfLine(QA),LengthOfLine(RA))",
"Equal(LengthOfLine(QT),86)",
"Equal(LengthOfLine(RS),54)",
"IsMidsegmentOfQuadrilateral(JK,AQTB)"
],
"image_cdl": [
"Equal(LengthOfLine(BT),LengthOfLine(SB))",
"Equal(LengthOfLine(QA),LengthOfLine(RA))",
"Equal(LengthOfLine(QT),86)",
"Equal(LengthOfLine(RS),54)"
],
"goal_cdl": "Value(LengthOfLine(JK))"
} | As shown in the diagram, BT=SB, QA=RA, QT=86, RS=54, the midsegment of quadrilateral AQTB is JK. Find the length of line JK. | 如图所示，BT=SB，QA=RA，QT=86，RS=54，JK是四边形AQTB的中位线。求直线JK的长度。 | 78 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-0.7071067811865477, -0.7071067811865475], "S": [-1.8369701987210297e-16, -1.0], "T": [0.7071067811865474, -0.7071067811865477], "X": [-1.0, 1.2246467991473532e-16], "Y": [-0.5000000000000004, -0.8660254037844384], "Z": [0.5000000000000001, -0.8660254037844386], "M": [1.0, 0.0], "N": [0.30901699437494745, 0.9510565162951535], "P": [-0.8090169943749473, 0.5877852522924732], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [0.7071067811865476, 0.7071067811865475], "J": [6.123233995736766e-17, 1.0], "K": [-0.7071067811865475, 0.7071067811865476]}
shapes = [["R", "A", "A", "B", "B", "S", "S", "R"], ["A", "J", "J", "K", "K", "B", "B", "A"], ["J", "Q", "Q", "T", "T", "K", "K", "J"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 3')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
4 | {
"construction_cdl": [
"Shape(WX,XY,YZ,ZW)"
],
"text_cdl": [
"Equal(LengthOfLine(WZ),23)",
"Equal(LengthOfLine(XY),23)",
"Equal(MeasureOfAngle(ZWX),112)",
"ParallelBetweenLine(XW,YZ)",
"Trapezoid(XYZW)"
],
"image_cdl": [
"Equal(LengthOfLine(WZ),23)",
"Equal(LengthOfLine(XY),23)",
"Equal(MeasureOfAngle(ZWX),112)",
"ParallelBetweenLine(XW,YZ)"
],
"goal_cdl": "Value(MeasureOfAngle(YZW))"
} | As shown in the diagram, WZ=23, XY=23, ∠ZWX=112°, XW is parallel to YZ, XYZW is a trapezoid. Find the measure of ∠YZW. | 如图所示，WZ=23，XY=23，∠ZWX=112°，XW平行于YZ，XY和ZW是梯形XYZW的腰。求∠YZW的大小。 | 68 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-0.7071067811865477, -0.7071067811865475], "S": [-1.8369701987210297e-16, -1.0], "T": [0.7071067811865474, -0.7071067811865477], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [1.0, 0.0], "N": [0.30901699437494745, 0.9510565162951535], "P": [-0.8090169943749473, 0.5877852522924732], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [0.7071067811865476, 0.7071067811865475], "J": [6.123233995736766e-17, 1.0], "K": [-0.7071067811865475, 0.7071067811865476], "W": [1.0, 0.0]}
shapes = [["W", "X", "X", "Y", "Y", "Z", "Z", "W"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 4')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
5 | {
"construction_cdl": [
"Shape(CA,AB,BC)",
"Shape(CB,BD,DC)",
"Collinear(ABD)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AD),z)",
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(BD),4)",
"Equal(LengthOfLine(CD),10)",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(DC,AC)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AD),z)",
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(BD),4)",
"Equal(LengthOfLine(CD),10)",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(DC,AC)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=y, AD=z, BC=x, BD=4, CD=10, AB⊥CB, DC⊥AC. Find the value of x. | 如图所示，AB=y，AD=z，BC=x，BD=4，CD=10，AB⊥CB，DC垂直于AC。求x的值。 | 2*sqrt(21) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-0.7071067811865477, -0.7071067811865475], "S": [-1.8369701987210297e-16, -1.0], "T": [0.7071067811865474, -0.7071067811865477], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [1.0, 0.0], "N": [0.30901699437494745, 0.9510565162951535], "P": [-0.8090169943749473, 0.5877852522924732], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [6.123233995736766e-17, 1.0], "K": [-0.7071067811865475, 0.7071067811865476], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0]}
shapes = [["C", "A", "A", "B", "B", "C"], ["C", "B", "B", "D", "D", "C"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 5')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
6 | {
"construction_cdl": [
"Shape(AC,CM,MA)",
"Shape(AM,MB,BA)",
"Collinear(CMB)"
],
"text_cdl": [
"Equal(LengthOfLine(AC),20)",
"Equal(LengthOfLine(CM),12)",
"Equal(LengthOfLine(MB),30)",
"PerpendicularBetweenLine(CM,AM)"
],
"image_cdl": [
"Equal(LengthOfLine(AC),20)",
"Equal(LengthOfLine(CM),12)",
"Equal(LengthOfLine(MB),30)",
"PerpendicularBetweenLine(CM,AM)"
],
"goal_cdl": "Value(PerimeterOfTriangle(AMB))"
} | As shown in the diagram, AC=20, CM=12, MB=30, CM is perpendicular to AM. Find the perimeter of △AMB. | 如图所示，AC=20，CM=12，MB=30，CM⊥AM。求三角形AMB的周长。 | 80 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-0.7071067811865477, -0.7071067811865475], "S": [-1.8369701987210297e-16, -1.0], "T": [0.7071067811865474, -0.7071067811865477], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-1.8369701987210297e-16, -1.0], "N": [0.30901699437494745, 0.9510565162951535], "P": [-0.8090169943749473, 0.5877852522924732], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [6.123233995736766e-17, 1.0], "K": [-0.7071067811865475, 0.7071067811865476], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0]}
shapes = [["A", "C", "C", "M", "M", "A"], ["A", "M", "M", "B", "B", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 6')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
7 | {
"construction_cdl": [
"Shape(TR,RS,ST)"
],
"text_cdl": [
"Equal(LengthOfLine(TR),7*sqrt(2))",
"Equal(LengthOfLine(TS),3*sqrt(2))",
"PerpendicularBetweenLine(RS,TS)"
],
"image_cdl": [
"Equal(LengthOfLine(TR),7*sqrt(2))",
"Equal(LengthOfLine(TS),3*sqrt(2))",
"PerpendicularBetweenLine(RS,TS)"
],
"goal_cdl": "Value(MeasureOfAngle(STR))"
} | As shown in the diagram, TR=7*sqrt(2), TS=3*sqrt(2), RS is perpendicular to TS. Find the measure of ∠STR. | 如图所示，TR=7*sqrt(2)，TS=3*sqrt(2)，RS垂直于TS。求∠STR的大小。 | 180*asin(2*sqrt(10)/7)/pi | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-1.8369701987210297e-16, -1.0], "N": [0.30901699437494745, 0.9510565162951535], "P": [-0.8090169943749473, 0.5877852522924732], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [6.123233995736766e-17, 1.0], "K": [-0.7071067811865475, 0.7071067811865476], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0]}
shapes = [["T", "R", "R", "S", "S", "T"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 7')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
8 | {
"construction_cdl": [
"Shape(AC,CB,BA)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),4/7)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),5/7)",
"PerpendicularBetweenLine(BA,CA)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),4/7)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),5/7)",
"PerpendicularBetweenLine(BA,CA)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=4/7, AC=x, BC=5/7, BA⊥CA. Find the value of x. | 如图所示，AB=4/7，AC=x，BC=5/7，BA垂直于CA。求x的值。 | 3/7 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-1.8369701987210297e-16, -1.0], "N": [0.30901699437494745, 0.9510565162951535], "P": [-0.8090169943749473, 0.5877852522924732], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [6.123233995736766e-17, 1.0], "K": [-0.7071067811865475, 0.7071067811865476], "W": [1.0, 0.0], "C": [-0.5000000000000004, -0.8660254037844384], "D": [-1.8369701987210297e-16, -1.0]}
shapes = [["A", "C", "C", "B", "B", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 8')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
9 | {
"construction_cdl": [
"Shape(KJM,MK,KJ)",
"Shape(MP,PK,KM)",
"Shape(KML,LP,PM)",
"Shape(PL,LN,NP)",
"Shape(KLN,NL)",
"Shape(PN,KNJ,JK,KP)",
"Collinear(JKPL)",
"Collinear(MPN)",
"Cocircular(K,JMLN)"
],
"text_cdl": [
"Equal(LengthOfLine(JK),10)",
"Equal(LengthOfLine(MN),16)",
"Equal(MeasureOfArc(KMN),98)",
"IsCentreOfCircle(K,K)",
"PerpendicularBetweenLine(MP,KP)"
],
"image_cdl": [
"Equal(LengthOfLine(JK),10)",
"IsCentreOfCircle(K,K)",
"PerpendicularBetweenLine(MP,KP)"
],
"goal_cdl": "Value(LengthOfLine(LN))"
} | As shown in the diagram, JK=10, MN=16, the measure of ⌒KMN is 98, the center of circle K is K, MP⊥KP. Find the length of line LN. | 如图所示，JK=10，MN=16，⌒KMN的角度为98，⊙K的圆心为K，MP垂直于KP。求直线LN的长度。 | 4*sqrt(5) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.5000000000000004, -0.8660254037844384], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [0.5000000000000001, 0.8660254037844386], "W": [1.0, 0.0], "C": [-0.5000000000000004, -0.8660254037844384], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.4999999999999998, 0.8660254037844387]}
shapes = [["K", "J", "M", "M", "K", "K", "J"], ["M", "P", "P", "K", "K", "M"], ["K", "M", "L", "L", "P", "P", "M"], ["P", "L", "L", "N", "N", "P"], ["K", "L", "N", "N", "L"], ["P", "N", "K", "N", "J", "J", "K", "K", "P"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 9')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
10 | {
"construction_cdl": [
"Shape(EDB,BF,EFD)",
"Shape(CD,EFD,FC)",
"Shape(FB,EBF)",
"Collinear(BFC)",
"Cocircular(E,FDB)"
],
"text_cdl": [
"Equal(MeasureOfAngle(FCD),x)",
"Equal(MeasureOfArc(EDB),10*x)",
"Equal(MeasureOfArc(EFD),40)",
"IsTangentOfCircle(CD,E)"
],
"image_cdl": [
"Equal(MeasureOfAngle(FCD),x)",
"Equal(MeasureOfArc(EDB),10*x)",
"Equal(MeasureOfArc(EFD),40)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, ∠FCD=x°, the measure of arc EDB is 10*x, the measure of arc EFD is 40, CD is the tangent to circle E. Find the value of x. | 如图所示，∠FCD=x°，弧EDB的角度为10*x，弧EFD的角度为40，圆O的切线为CD。求x的值。 | 5 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.5000000000000004, -0.8660254037844384], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [1.0, 0.0], "J": [1.0, 0.0], "K": [0.5000000000000001, 0.8660254037844386], "W": [1.0, 0.0], "C": [0.30901699437494745, 0.9510565162951535], "D": [-0.8090169943749473, 0.5877852522924732], "L": [-0.4999999999999998, 0.8660254037844387], "E": [-0.8090169943749476, -0.587785252292473], "F": [0.30901699437494723, -0.9510565162951536]}
shapes = [["E", "D", "B", "B", "F", "E", "F", "D"], ["C", "D", "E", "F", "D", "F", "C"], ["F", "B", "E", "B", "F"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 10')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
11 | {
"construction_cdl": [
"Shape(KA,AH,HK)",
"Shape(KH,HC,CK)",
"Shape(KC,CF,FK)",
"Shape(KF,FG,GK)",
"Shape(GF,FE,EG)",
"Collinear(AHCF)",
"Collinear(EGK)"
],
"text_cdl": [
"Equal(MeasureOfAngle(CFK),28)",
"Equal(MeasureOfAngle(GKF),35)",
"Equal(MeasureOfAngle(KAC),25)",
"Equal(MeasureOfAngle(KHC),51)",
"PerpendicularBetweenLine(EG,FG)",
"PerpendicularBetweenLine(HC,KC)",
"PerpendicularBetweenLine(KF,EF)"
],
"image_cdl": [
"Equal(MeasureOfAngle(CFK),28)",
"Equal(MeasureOfAngle(GKF),35)",
"Equal(MeasureOfAngle(KAC),25)",
"Equal(MeasureOfAngle(KHC),51)",
"PerpendicularBetweenLine(EG,FG)",
"PerpendicularBetweenLine(HC,KC)",
"PerpendicularBetweenLine(KF,EF)"
],
"goal_cdl": "Value(MeasureOfAngle(FEK))"
} | As shown in the diagram, ∠CFK=28°, ∠GKF=35°, ∠KAC=25°, ∠KHC=51°, EG is perpendicular to FG, HC is perpendicular to KC, KF is perpendicular to EF. Find the measure of ∠FEK. | 如图所示，∠CFK=28°，∠GKF=35°，∠KAC=25°，∠KHC=51°，EG⊥FG，HC垂直于KC，KF垂直于EF。求∠FEK的大小。 | 55 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.5000000000000004, -0.8660254037844384], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [1.0, 0.0], "J": [1.0, 0.0], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [0.6234898018587336, 0.7818314824680298], "D": [-0.8090169943749473, 0.5877852522924732], "L": [-0.4999999999999998, 0.8660254037844387], "E": [-0.22252093395631434, 0.9749279121818236], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236]}
shapes = [["K", "A", "A", "H", "H", "K"], ["K", "H", "H", "C", "C", "K"], ["K", "C", "C", "F", "F", "K"], ["K", "F", "F", "G", "G", "K"], ["G", "F", "F", "E", "E", "G"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 11')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
12 | {
"construction_cdl": [
"Shape(XBY,YM,MB)",
"Shape(XYA,AM,MY)",
"Shape(XM,MA,XAC,CN,NX)",
"Shape(NC,XCZ,ZN)",
"Shape(NZ,XZD,DN)",
"Shape(MX,XN,ND,XDB,BM)",
"Collinear(AMB)",
"Collinear(YMX)",
"Collinear(XNZ)",
"Collinear(CND)",
"Cocircular(X,ACZDBY)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),30)",
"Equal(LengthOfLine(CD),30)",
"Equal(MeasureOfArc(XCZ),40)",
"IsCentreOfCircle(X,X)",
"PerpendicularBetweenLine(AM,YM)",
"PerpendicularBetweenLine(DN,ZN)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),30)",
"Equal(LengthOfLine(CD),30)",
"Equal(MeasureOfArc(XCZ),40)",
"IsCentreOfCircle(X,X)",
"PerpendicularBetweenLine(AM,YM)",
"PerpendicularBetweenLine(DN,ZN)"
],
"goal_cdl": "Value(MeasureOfArc(XBA))"
} | As shown in the diagram, AB=30, CD=30, the measure of arc XCZ is 40, the center of ⊙X is X, AM is perpendicular to YM, DN⊥ZN. Find the measure of arc XBA. | 如图所示，AB=30，CD=30，⌒XCZ的角度为40，⊙X的圆心为X，AM垂直于YM，DN⊥ZN。求弧XBA的角度。 | 80 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [-0.5000000000000004, -0.8660254037844384], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [-0.9396926207859083, 0.3420201433256689], "N": [-0.9396926207859084, -0.34202014332566866], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [0.766044443118978, 0.6427876096865393], "J": [1.0, 0.0], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [0.17364817766693041, 0.984807753012208], "D": [-0.4999999999999998, 0.8660254037844387], "L": [-0.4999999999999998, 0.8660254037844387], "E": [-0.22252093395631434, 0.9749279121818236], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236]}
shapes = [["X", "B", "Y", "Y", "M", "M", "B"], ["X", "Y", "A", "A", "M", "M", "Y"], ["X", "M", "M", "A", "X", "A", "C", "C", "N", "N", "X"], ["N", "C", "X", "C", "Z", "Z", "N"], ["N", "Z", "X", "Z", "D", "D", "N"], ["M", "X", "X", "N", "N", "D", "X", "D", "B", "B", "M"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 12')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
13 | {
"construction_cdl": [
"Shape(XDB,BD)",
"Shape(BA,AC,XBC)",
"Shape(DB,XBC,CE,XED)",
"Shape(XCE,EC)",
"Collinear(ABXD)",
"Collinear(ACE)",
"Cocircular(X,BCED)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),5)",
"Equal(LengthOfLine(BD),x)",
"Equal(LengthOfLine(CA),15/2)",
"Equal(LengthOfLine(EC),9/2)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),5)",
"Equal(LengthOfLine(BD),x)",
"Equal(LengthOfLine(CA),15/2)",
"Equal(LengthOfLine(EC),9/2)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=5, BD=x, CA=15/2, EC=9/2. Find the value of x. | 如图所示，AB=5，BD=x，CA=15/2，EC=9/2。求x的值。 | 13 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [0.5000000000000001, -0.8660254037844386], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [-0.9396926207859083, 0.3420201433256689], "N": [-0.9396926207859084, -0.34202014332566866], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [0.5000000000000001, 0.8660254037844386], "J": [1.0, 0.0], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [-0.4999999999999998, 0.8660254037844387], "D": [-1.0, 1.2246467991473532e-16], "L": [-0.4999999999999998, 0.8660254037844387], "E": [-0.5000000000000004, -0.8660254037844384], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236]}
shapes = [["X", "D", "B", "B", "D"], ["B", "A", "A", "C", "X", "B", "C"], ["D", "B", "X", "B", "C", "C", "E", "X", "E", "D"], ["X", "C", "E", "E", "C"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 13')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
14 | {
"construction_cdl": [
"Shape(AC,CJ,JA)",
"Shape(JC,CB,BJ)",
"Shape(AJ,JD,DA)",
"Shape(JB,BD,DJ)",
"Collinear(AJB)",
"Collinear(CJD)"
],
"text_cdl": [
"Equal(LengthOfLine(AJ),2*x+3)",
"Equal(LengthOfLine(CJ),8*y-36)",
"Equal(LengthOfLine(JB),5*x)",
"Equal(LengthOfLine(JD),4*y)",
"Parallelogram(ACBD)"
],
"image_cdl": [
"Equal(LengthOfLine(AJ),2*x+3)",
"Equal(LengthOfLine(CJ),8*y-36)",
"Equal(LengthOfLine(JB),5*x)",
"Equal(LengthOfLine(JD),4*y)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, AJ=2*x+3, CJ=8*y-36, JB=5*x, JD=4*y, quadrilateral ACBD is a parallelogram. Find the value of y. | 如图所示，AJ=2*x+3，CJ=8*y-36，JB=5*x，JD=4*y，AD和CB是▱ACBD的一组对边。求y的值。 | 9 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [0.5000000000000001, -0.8660254037844386], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [-0.9396926207859083, 0.3420201433256689], "N": [-0.9396926207859084, -0.34202014332566866], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [0.30901699437494745, 0.9510565162951535], "J": [0.30901699437494723, -0.9510565162951536], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [-0.8090169943749473, 0.5877852522924732], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.4999999999999998, 0.8660254037844387], "E": [-0.5000000000000004, -0.8660254037844384], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236]}
shapes = [["A", "C", "C", "J", "J", "A"], ["J", "C", "C", "B", "B", "J"], ["A", "J", "J", "D", "D", "A"], ["J", "B", "B", "D", "D", "J"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 14')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
15 | {
"construction_cdl": [
"Shape(JI,IL,LN,NJ)",
"Shape(IB,BD,DL,LI)",
"Shape(CJ,JN)",
"Collinear(CJIB)",
"Collinear(NLD)"
],
"text_cdl": [
"Equal(LengthOfLine(IB),1/2*x-7)",
"Equal(LengthOfLine(JI),1/4*x+5)",
"Equal(LengthOfLine(LD),66-2/3*y)",
"Equal(LengthOfLine(NL),1/3*y-6)",
"Equal(LengthOfLine(NL),LengthOfLine(LD))",
"PerpendicularBetweenLine(CJ,NJ)",
"PerpendicularBetweenLine(IB,DB)",
"PerpendicularBetweenLine(JI,LI)"
],
"image_cdl": [
"Equal(LengthOfLine(IB),1/2*x-7)",
"Equal(LengthOfLine(JI),1/4*x+5)",
"Equal(LengthOfLine(LD),66-2/3*y)",
"Equal(LengthOfLine(NL),1/3*y-6)",
"Equal(LengthOfLine(NL),LengthOfLine(LD))",
"PerpendicularBetweenLine(CJ,NJ)",
"PerpendicularBetweenLine(IB,DB)",
"PerpendicularBetweenLine(JI,LI)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, IB=1/2*x-7, JI=1/4*x+5, LD=66-2/3*y, NL=1/3*y-6, NL=LD, CJ⊥NJ, IB is perpendicular to DB, JI is perpendicular to LI. Find the value of x. | 如图所示，IB=1/2*x-7，JI=1/4*x+5，LD=66-2/3*y，NL=1/3*y-6，NL=LD，CJ⊥NJ，IB⊥DB，JI垂直于LI。求x的值。 | 48 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [0.5000000000000001, -0.8660254037844386], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [-0.9396926207859083, 0.3420201433256689], "N": [0.6234898018587334, -0.7818314824680299], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [1.0, 0.0], "J": [-0.9009688679024191, -0.433883739117558], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [0.6234898018587336, 0.7818314824680298], "D": [-0.22252093395631434, 0.9749279121818236], "L": [-0.2225209339563146, -0.9749279121818236], "E": [-0.5000000000000004, -0.8660254037844384], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236], "I": [-0.900968867902419, 0.43388373911755823]}
shapes = [["J", "I", "I", "L", "L", "N", "N", "J"], ["I", "B", "B", "D", "D", "L", "L", "I"], ["C", "J", "J", "N"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 15')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
16 | {
"construction_cdl": [
"Shape(AB,BC,CA)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),y)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(ABC),60)",
"PerpendicularBetweenLine(BC,AC)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),y)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(ABC),60)",
"PerpendicularBetweenLine(BC,AC)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, AB=10, AC=y, BC=x, ∠ABC=60°, BC is perpendicular to AC. Find the value of y. | 如图所示，AB=10，AC=y，BC=x，∠ABC=60°，BC垂直于AC。求y的值。 | 5*sqrt(3) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [0.5000000000000001, -0.8660254037844386], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [-0.9396926207859083, 0.3420201433256689], "N": [0.6234898018587334, -0.7818314824680299], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [-0.9009688679024191, -0.433883739117558], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [-0.5000000000000004, -0.8660254037844384], "D": [-0.22252093395631434, 0.9749279121818236], "L": [-0.2225209339563146, -0.9749279121818236], "E": [-0.5000000000000004, -0.8660254037844384], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236], "I": [-0.900968867902419, 0.43388373911755823]}
shapes = [["A", "B", "B", "C", "C", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 16')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
17 | {
"construction_cdl": [
"Shape(CB,BE,ED,DC)",
"Shape(BA,AE,EB)",
"Collinear(ABC)",
"Collinear(AED)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(AD),27)",
"Equal(LengthOfLine(AE),12)",
"ParallelBetweenLine(CD,BE)"
],
"image_cdl": [
"ParallelBetweenLine(CD,BE)"
],
"goal_cdl": "Value(LengthOfLine(BC))"
} | As shown in the diagram, AB=8, AD=27, AE=12, CD is parallel to BE. Find the length of line BC. | 如图所示，AB=8，AD=27，AE=12，CD平行于BE。求直线BC的长度。 | 10 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [0.5000000000000001, -0.8660254037844386], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [-0.9396926207859083, 0.3420201433256689], "N": [0.6234898018587334, -0.7818314824680299], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.0, 1.2246467991473532e-16], "A": [1.0, 0.0], "B": [0.30901699437494745, 0.9510565162951535], "J": [-0.9009688679024191, -0.433883739117558], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [-0.8090169943749473, 0.5877852522924732], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236], "I": [-0.900968867902419, 0.43388373911755823]}
shapes = [["C", "B", "B", "E", "E", "D", "D", "C"], ["B", "A", "A", "E", "E", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 17')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
18 | {
"construction_cdl": [
"Shape(MQ,QP,PN,NM)"
],
"text_cdl": [
"Equal(MeasureOfAngle(NMQ),10*x)",
"Equal(MeasureOfAngle(PNM),20*x)",
"Equal(MeasureOfAngle(PNM),MeasureOfAngle(MQP))",
"Equal(MeasureOfAngle(QPN),MeasureOfAngle(NMQ))",
"Parallelogram(MQPN)"
],
"image_cdl": [
"Equal(MeasureOfAngle(PNM),MeasureOfAngle(MQP))",
"Equal(MeasureOfAngle(QPN),MeasureOfAngle(NMQ))"
],
"goal_cdl": "Value(MeasureOfAngle(MQP))"
} | As shown in the diagram, ∠NMQ=10*x°, ∠PNM=20*x°, ∠PNM=∠MQP, ∠QPN=∠NMQ, MQPN is a parallelogram. Find the measure of ∠MQP. | 如图所示，∠NMQ=10*x°，∠PNM=20*x°，∠PNM=∠MQP，∠QPN=∠NMQ，四边形MQPN是平行四边形。求∠MQP的大小。 | 120 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [0.5000000000000001, -0.8660254037844386], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [1.0, 0.0], "N": [6.123233995736766e-17, 1.0], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [0.30901699437494745, 0.9510565162951535], "J": [-0.9009688679024191, -0.433883739117558], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [-0.8090169943749473, 0.5877852522924732], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236], "I": [-0.900968867902419, 0.43388373911755823]}
shapes = [["M", "Q", "Q", "P", "P", "N", "N", "M"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 18')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
19 | {
"construction_cdl": [
"Shape(AC,CB,BA)",
"Shape(BC,CD,DB)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),4*x-17)",
"Equal(LengthOfLine(CD),2*x-1)",
"Equal(MeasureOfAngle(BCD),4*y-19)",
"Equal(MeasureOfAngle(CBA),3*y+3)",
"Parallelogram(ACDB)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),4*x-17)",
"Equal(LengthOfLine(CD),2*x-1)",
"Equal(MeasureOfAngle(BCD),4*y-19)",
"Equal(MeasureOfAngle(CBA),3*y+3)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, AB=4*x-17, CD=2*x-1, ∠BCD=4*y-19°, ∠CBA=3*y+3°, quadrilateral ACDB is a ▱. Find the value of y. | 如图所示，AB=4*x-17，CD=2*x-1，∠BCD=4*y-19°，∠CBA=3*y+3°，AB和CD是▱ACDB的一组对边。求y的值。 | 22 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [0.5000000000000001, -0.8660254037844386], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [1.0, 0.0], "N": [6.123233995736766e-17, 1.0], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [-0.9009688679024191, -0.433883739117558], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236], "I": [-0.900968867902419, 0.43388373911755823]}
shapes = [["A", "C", "C", "B", "B", "A"], ["B", "C", "C", "D", "D", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 19')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
20 | {
"construction_cdl": [
"Shape(AD,DE,EA)",
"Shape(AE,EB,BA)",
"Shape(ED,DC,CE)",
"Shape(BE,EC,CB)",
"Collinear(DEB)",
"Collinear(AEC)"
],
"text_cdl": [
"Equal(LengthOfLine(AE),LengthOfLine(BE))",
"Equal(LengthOfLine(BA),8)",
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BE),LengthOfLine(CE))",
"Equal(LengthOfLine(DA),10)",
"Equal(LengthOfLine(DC),10)",
"Equal(MeasureOfAngle(ADE),x)",
"PerpendicularBetweenLine(DE,AE)"
],
"image_cdl": [
"Equal(LengthOfLine(AE),LengthOfLine(BE))",
"Equal(LengthOfLine(BA),8)",
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BE),LengthOfLine(CE))",
"Equal(LengthOfLine(DA),10)",
"Equal(LengthOfLine(DC),10)",
"Equal(MeasureOfAngle(ADE),x)",
"PerpendicularBetweenLine(DE,AE)"
],
"goal_cdl": "Value(Sin(x))"
} | As shown in the diagram, AE=BE, BA=8, BC=8, BE=CE, DA=10, DC=10, ∠ADE=x°, DE⊥AE. Find sin(x). | 如图所示，AE=BE，BA=8，BC=8，BE=CE，DA=10，DC=10，∠ADE=x°，DE垂直于AE。求sin(x)。 | 2*sqrt(2)/5 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [0.5000000000000001, -0.8660254037844386], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [1.0, 0.0], "N": [6.123233995736766e-17, 1.0], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [0.30901699437494745, 0.9510565162951535], "J": [-0.9009688679024191, -0.433883739117558], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [-0.8090169943749473, 0.5877852522924732], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236], "I": [-0.900968867902419, 0.43388373911755823]}
shapes = [["A", "D", "D", "E", "E", "A"], ["A", "E", "E", "B", "B", "A"], ["E", "D", "D", "C", "C", "E"], ["B", "E", "E", "C", "C", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 20')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
21 | {
"construction_cdl": [
"Shape(AB,BX,XC,CA)"
],
"text_cdl": [
"Equal(MeasureOfAngle(ABX),5*y-6)",
"Equal(MeasureOfAngle(BXC),2*x+24)",
"Equal(MeasureOfAngle(CAB),3*x-17)",
"Equal(MeasureOfAngle(XCA),y+58)",
"Parallelogram(ABXC)"
],
"image_cdl": [
"Equal(MeasureOfAngle(ABX),5*y-6)",
"Equal(MeasureOfAngle(BXC),2*x+24)",
"Equal(MeasureOfAngle(CAB),3*x-17)",
"Equal(MeasureOfAngle(XCA),y+58)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, ∠ABX=5*y-6°, ∠BXC=2*x+24°, ∠CAB=3*x-17°, ∠XCA=y+58°, BA and XC are opposite sides of the ▱ ABXC. Find the value of y. | 如图所示，∠ABX=5*y-6°，∠BXC=2*x+24°，∠CAB=3*x-17°，∠XCA=y+58°，BA和XC是▱ABXC的一组对边。求y的值。 | 16 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [1.0, 0.0], "N": [6.123233995736766e-17, 1.0], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [-0.9009688679024191, -0.433883739117558], "K": [0.6234898018587334, -0.7818314824680299], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.900968867902419, 0.43388373911755823], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.2225209339563146, -0.9749279121818236], "I": [-0.900968867902419, 0.43388373911755823]}
shapes = [["A", "B", "B", "X", "X", "C", "C", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 21')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
22 | {
"construction_cdl": [
"Shape(KJ,JE)",
"Shape(EJ,JA)",
"Shape(AJ,JN)",
"Shape(NJ,JK)",
"Shape(HN,NJ)",
"Shape(JN,NF)",
"Shape(FN,NI)",
"Shape(IN,NH)",
"Collinear(KJA)",
"Collinear(HNF)",
"Collinear(EJNI)"
],
"text_cdl": [
"Equal(MeasureOfAngle(NJK),101)",
"ParallelBetweenLine(JA,NF)"
],
"image_cdl": [
"ParallelBetweenLine(JA,NF)"
],
"goal_cdl": "Value(MeasureOfAngle(HNJ))"
} | As shown in the diagram, ∠NJK=101°, JA is parallel to NF. Find the measure of ∠HNJ. | 如图所示，∠NJK=101°，JA∥NF。求∠HNJ的大小。 | 79 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [1.0, 0.0], "N": [0.7071067811865474, -0.7071067811865477], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [-0.7071067811865477, -0.7071067811865475], "K": [-1.8369701987210297e-16, -1.0], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.7071067811865476, 0.7071067811865475], "F": [6.123233995736766e-17, 1.0], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.7071067811865475, 0.7071067811865476], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["K", "J", "J", "E"], ["E", "J", "J", "A"], ["A", "J", "J", "N"], ["N", "J", "J", "K"], ["H", "N", "N", "J"], ["J", "N", "N", "F"], ["F", "N", "N", "I"], ["I", "N", "N", "H"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 22')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
23 | {
"construction_cdl": [
"Shape(RS,ST,TR)"
],
"text_cdl": [
"Equal(LengthOfLine(SR),3*x-5)",
"Equal(LengthOfLine(TR),2*x+7)",
"Equal(LengthOfLine(TS),22)",
"IsoscelesTriangle(RST)"
],
"image_cdl": [
"Equal(LengthOfLine(SR),3*x-5)",
"Equal(LengthOfLine(TR),2*x+7)",
"Equal(LengthOfLine(TS),22)"
],
"goal_cdl": "Value(LengthOfLine(RS))"
} | As shown in the diagram, SR=3*x-5, TR=2*x+7, TS=22, RS and RT are the legs of the isosceles △ RST. Find the length of line RS. | 如图所示，SR=3*x-5，TR=2*x+7，TS=22，∠RST和∠STR是等腰△RST的底角。求直线RS的长度。 | 31 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.17364817766692997, -0.9848077530122081], "Z": [0.7660444431189778, -0.6427876096865396], "M": [1.0, 0.0], "N": [0.7071067811865474, -0.7071067811865477], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [-0.7071067811865477, -0.7071067811865475], "K": [-1.8369701987210297e-16, -1.0], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.7071067811865476, 0.7071067811865475], "F": [6.123233995736766e-17, 1.0], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.7071067811865475, 0.7071067811865476], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["R", "S", "S", "T", "T", "R"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 23')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
24 | {
"construction_cdl": [
"Shape(WZ,ZY,YX,XW)"
],
"text_cdl": [
"Equal(LengthOfLine(YX),24)",
"Equal(LengthOfLine(YZ),28)",
"Equal(MeasureOfAngle(XWZ),105)",
"Parallelogram(WZYX)"
],
"image_cdl": [
"Equal(LengthOfLine(YX),24)",
"Equal(LengthOfLine(YZ),28)",
"Equal(MeasureOfAngle(XWZ),105)"
],
"goal_cdl": "Value(MeasureOfAngle(WZY))"
} | As shown in the diagram, YX=24, YZ=28, ∠XWZ=105°, quadrilateral WZYX is a ▱. Find the measure of ∠WZY. | 如图所示，YX=24，YZ=28，∠XWZ=105°，WX和ZY是平行四边形WZYX的一组对边。求∠WZY的大小。 | 75 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [1.0, 0.0], "N": [0.7071067811865474, -0.7071067811865477], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [-0.7071067811865477, -0.7071067811865475], "K": [-1.8369701987210297e-16, -1.0], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.7071067811865476, 0.7071067811865475], "F": [6.123233995736766e-17, 1.0], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.7071067811865475, 0.7071067811865476], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["W", "Z", "Z", "Y", "Y", "X", "X", "W"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 24')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
25 | {
"construction_cdl": [
"Shape(CA,AD,DC)",
"Shape(DA,AB,BD)",
"Collinear(BDC)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AD),3*sqrt(3))",
"Equal(LengthOfLine(BD),9)",
"Equal(LengthOfLine(CD),y)",
"Equal(MeasureOfAngle(ABC),30)",
"Equal(MeasureOfAngle(BCA),60)",
"PerpendicularBetweenLine(AD,CD)",
"PerpendicularBetweenLine(CA,BA)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AD),3*sqrt(3))",
"Equal(LengthOfLine(BD),9)",
"Equal(LengthOfLine(CD),y)",
"Equal(MeasureOfAngle(ABC),30)",
"Equal(MeasureOfAngle(BCA),60)",
"PerpendicularBetweenLine(AD,CD)",
"PerpendicularBetweenLine(CA,BA)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=x, AD=3*sqrt(3), BD=9, CD=y, ∠ABC=30°, ∠BCA=60°, AD is perpendicular to CD, CA is perpendicular to BA. Find the value of x. | 如图所示，AB=x，AD=3*sqrt(3)，BD=9，CD=y，∠ABC=30°，∠BCA=60°，AD⊥CD，CA垂直于BA。求x的值。 | 6*sqrt(3) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [1.0, 0.0], "N": [0.7071067811865474, -0.7071067811865477], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [-0.7071067811865477, -0.7071067811865475], "K": [-1.8369701987210297e-16, -1.0], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.7071067811865476, 0.7071067811865475], "F": [6.123233995736766e-17, 1.0], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.7071067811865475, 0.7071067811865476], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["C", "A", "A", "D", "D", "C"], ["D", "A", "A", "B", "B", "D"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 25')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
26 | {
"construction_cdl": [
"Shape(AB,BC,CA)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),18)",
"Equal(MeasureOfAngle(ABC),30)",
"PerpendicularBetweenLine(CA,BA)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),18)",
"Equal(MeasureOfAngle(ABC),30)",
"PerpendicularBetweenLine(CA,BA)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, AB=y, AC=x, BC=18, ∠ABC=30°, CA is perpendicular to BA. Find the value of y. | 如图所示，AB=y，AC=x，BC=18，∠ABC=30°，CA⊥BA。求y的值。 | 9*sqrt(3) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [1.0, 0.0], "N": [0.7071067811865474, -0.7071067811865477], "P": [-1.0, 1.2246467991473532e-16], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [-0.7071067811865477, -0.7071067811865475], "K": [-1.8369701987210297e-16, -1.0], "W": [1.0, 0.0], "C": [-0.5000000000000004, -0.8660254037844384], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.2225209339563146, -0.9749279121818236], "E": [0.7071067811865476, 0.7071067811865475], "F": [6.123233995736766e-17, 1.0], "G": [-0.9009688679024191, -0.433883739117558], "H": [-0.7071067811865475, 0.7071067811865476], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["A", "B", "B", "C", "C", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 26')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
27 | {
"construction_cdl": [
"Shape(HLJ,JH,HP,PL)",
"Shape(HJM,MP,PH,HJ)",
"Shape(HMK,KP,PM)",
"Shape(HKL,LP,PK)",
"Collinear(JHPK)",
"Collinear(LPM)",
"Cocircular(H,JMKL)"
],
"text_cdl": [
"Equal(DiameterOfCircle(H),18)",
"Equal(LengthOfLine(LM),12)",
"Equal(MeasureOfArc(HML),84)",
"IsCentreOfCircle(H,H)",
"PerpendicularBetweenLine(MP,HP)"
],
"image_cdl": [
"IsCentreOfCircle(H,H)",
"PerpendicularBetweenLine(MP,HP)"
],
"goal_cdl": "Value(MeasureOfArc(HKL))"
} | As shown in the diagram, the diameter of ⊙H is 18, LM=12, the measure of ⌒HML is 84, H is the center of circle H, MP⊥HP. Find the measure of ⌒HKL. | 如图所示，圆H的直径为18，LM=12，⌒HML的角度为84，⊙H的圆心为H，MP垂直于HP。求⌒HKL的角度。 | 42 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [-0.5000000000000004, -0.8660254037844384], "D": [-1.8369701987210297e-16, -1.0], "L": [-1.0, 1.2246467991473532e-16], "E": [0.7071067811865476, 0.7071067811865475], "F": [6.123233995736766e-17, 1.0], "G": [-0.9009688679024191, -0.433883739117558], "H": [1.0, 0.0], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["H", "L", "J", "J", "H", "H", "P", "P", "L"], ["H", "J", "M", "M", "P", "P", "H", "H", "J"], ["H", "M", "K", "K", "P", "P", "M"], ["H", "K", "L", "L", "P", "P", "K"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 27')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
28 | {
"construction_cdl": [
"Shape(GD,DF)",
"Shape(FD,DH)",
"Shape(DH,HA)",
"Shape(AH,HC)",
"Shape(CH,HE)",
"Shape(EH,HD)",
"Shape(HD,DB)",
"Shape(BD,DG)",
"Collinear(GDHC)",
"Collinear(FDB)",
"Collinear(AHE)"
],
"text_cdl": [
"Equal(MeasureOfAngle(CHE),9*x-11)",
"Equal(MeasureOfAngle(GDF),8*x+4)",
"ParallelBetweenLine(BD,EH)"
],
"image_cdl": [
"Equal(MeasureOfAngle(CHE),9*x-11)",
"Equal(MeasureOfAngle(GDF),8*x+4)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, ∠CHE=9*x-11°, ∠GDF=8*x+4°, BD is parallel to EH. Find the value of x. | 如图所示，∠CHE=9*x-11°，∠GDF=8*x+4°，BD∥EH。求x的值。 | 15 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [0.7071067811865476, 0.7071067811865475], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [6.123233995736766e-17, 1.0], "D": [-0.7071067811865475, 0.7071067811865476], "L": [-1.0, 1.2246467991473532e-16], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.7071067811865477, -0.7071067811865475], "G": [-1.8369701987210297e-16, -1.0], "H": [0.7071067811865474, -0.7071067811865477], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["G", "D", "D", "F"], ["F", "D", "D", "H"], ["D", "H", "H", "A"], ["A", "H", "H", "C"], ["C", "H", "H", "E"], ["E", "H", "H", "D"], ["H", "D", "D", "B"], ["B", "D", "D", "G"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 28')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
29 | {
"construction_cdl": [
"Shape(SR,RT,TS)"
],
"text_cdl": [
"Equal(LengthOfLine(RS),5)",
"Equal(LengthOfLine(TR),6)",
"Equal(LengthOfLine(TS),3)",
"Equal(MeasureOfAngle(SRT),x)"
],
"image_cdl": [
"Equal(LengthOfLine(RS),5)",
"Equal(LengthOfLine(TR),6)",
"Equal(LengthOfLine(TS),3)",
"Equal(MeasureOfAngle(SRT),x)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, RS=5, TR=6, TS=3, ∠SRT=x°. Find the value of x. | 如图所示，RS=5，TR=6，TS=3，∠SRT=x°。求x的值。 | 180*acos(13/15)/pi | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [0.7071067811865476, 0.7071067811865475], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [6.123233995736766e-17, 1.0], "D": [-0.7071067811865475, 0.7071067811865476], "L": [-1.0, 1.2246467991473532e-16], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.7071067811865477, -0.7071067811865475], "G": [-1.8369701987210297e-16, -1.0], "H": [0.7071067811865474, -0.7071067811865477], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["S", "R", "R", "T", "T", "S"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 29')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
30 | {
"construction_cdl": [
"Shape(CD,DE,EF,FC)",
"Shape(BL,LA,AN,NB)"
],
"text_cdl": [
"Equal(AreaOfQuadrilateral(BLAN),72)",
"Equal(AreaOfQuadrilateral(CDEF),50)",
"Equal(LengthOfLine(BN),6)",
"Equal(LengthOfLine(CF),x)",
"SimilarBetweenQuadrilateral(CDEF,BLAN)"
],
"image_cdl": [
"Equal(AreaOfQuadrilateral(BLAN),72)",
"Equal(AreaOfQuadrilateral(CDEF),50)",
"Equal(LengthOfLine(BN),6)",
"Equal(LengthOfLine(CF),x)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, the area of BLAN is 72, the area of quadrilateral CDEF is 50, BN=6, CF=x, CDEF is similar to BLAN. Find the value of x. | 如图所示，四边形BLAN的面积为72，CDEF的面积为50，BN=6，CF=x，CDEF相似于BLAN。求x的值。 | 5 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [0.7071067811865476, 0.7071067811865475], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [6.123233995736766e-17, 1.0], "D": [-0.7071067811865475, 0.7071067811865476], "L": [-1.8369701987210297e-16, -1.0], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.7071067811865477, -0.7071067811865475], "G": [-1.8369701987210297e-16, -1.0], "H": [0.7071067811865474, -0.7071067811865477], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["C", "D", "D", "E", "E", "F", "F", "C"], ["B", "L", "L", "A", "A", "N", "N", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 30')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
31 | {
"construction_cdl": [
"Shape(GC,CE)",
"Shape(EC,CA)",
"Shape(GC,CA)",
"Shape(EC,CD)",
"Shape(AC,CD)",
"Collinear(GCD)"
],
"text_cdl": [
"Equal(MeasureOfAngle(ACD),x)",
"Equal(MeasureOfAngle(ECA),2*x)",
"Equal(MeasureOfAngle(GCE),x)"
],
"image_cdl": [
"Equal(MeasureOfAngle(ACD),x)",
"Equal(MeasureOfAngle(ECA),2*x)",
"Equal(MeasureOfAngle(GCE),x)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, ∠ACD=x°, ∠ECA=2*x°, ∠GCE=x°. Find the value of x. | 如图所示，∠ACD=x°，∠ECA=2*x°，∠GCE=x°。求x的值。 | 45 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [0.7071067811865476, 0.7071067811865475], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [0.30901699437494745, 0.9510565162951535], "D": [-0.8090169943749473, 0.5877852522924732], "L": [-1.8369701987210297e-16, -1.0], "E": [-0.8090169943749476, -0.587785252292473], "F": [-0.7071067811865477, -0.7071067811865475], "G": [0.30901699437494723, -0.9510565162951536], "H": [0.7071067811865474, -0.7071067811865477], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["G", "C", "C", "E"], ["E", "C", "C", "A"], ["G", "C", "C", "A"], ["E", "C", "C", "D"], ["A", "C", "C", "D"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 31')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
32 | {
"construction_cdl": [
"Shape(DF,FH)",
"Shape(HF,FA)",
"Shape(AF,FB)",
"Shape(BF,FD)",
"Collinear(DFA)",
"Collinear(BFH)"
],
"text_cdl": [
"Equal(MeasureOfAngle(DFH),4*x)",
"Equal(MeasureOfAngle(HFA),2*x-6)"
],
"image_cdl": [],
"goal_cdl": "Value(MeasureOfAngle(DFH))"
} | As shown in the diagram, ∠DFH=4*x°, ∠HFA=2*x-6°. Find the measure of ∠DFH. | 如图所示，∠DFH=4*x°，∠HFA=2*x-6°。求∠DFH的大小。 | 124 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [0.30901699437494745, 0.9510565162951535], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [0.30901699437494745, 0.9510565162951535], "D": [-0.8090169943749473, 0.5877852522924732], "L": [-1.8369701987210297e-16, -1.0], "E": [-0.8090169943749476, -0.587785252292473], "F": [-0.8090169943749476, -0.587785252292473], "G": [0.30901699437494723, -0.9510565162951536], "H": [0.30901699437494723, -0.9510565162951536], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["D", "F", "F", "H"], ["H", "F", "F", "A"], ["A", "F", "F", "B"], ["B", "F", "F", "D"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 32')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
33 | {
"construction_cdl": [
"Shape(AD,DE,EA)",
"Shape(ED,DC,CE)",
"Shape(EC,CB,BE)",
"Shape(BA,AE,EB)",
"Collinear(AEC)",
"Collinear(DEB)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),2*x+3)",
"Equal(LengthOfLine(BC),5*x)",
"Rhombus(ADCB)"
],
"image_cdl": [],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=2*x+3, BC=5*x, ADCB is a rhombus. Find the value of x. | 如图所示，AB=2*x+3，BC=5*x，ADCB是菱形。求x的值。 | 1 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [0.30901699437494745, 0.9510565162951535], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [-0.8090169943749473, 0.5877852522924732], "D": [-0.8090169943749476, -0.587785252292473], "L": [-1.8369701987210297e-16, -1.0], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.8090169943749476, -0.587785252292473], "G": [0.30901699437494723, -0.9510565162951536], "H": [0.30901699437494723, -0.9510565162951536], "I": [-1.0, 1.2246467991473532e-16]}
shapes = [["A", "D", "D", "E", "E", "A"], ["E", "D", "D", "C", "C", "E"], ["E", "C", "C", "B", "B", "E"], ["B", "A", "A", "E", "E", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 33')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
34 | {
"construction_cdl": [
"Shape(OA,OAB,BO)",
"Shape(AO,OB,OBA)",
"Cocircular(O,AB)"
],
"text_cdl": [
"Equal(LengthOfLine(OA),3)",
"Equal(MeasureOfAngle(AOB),45)",
"IsCentreOfCircle(O,O)"
],
"image_cdl": [
"Equal(LengthOfLine(OA),3)",
"Equal(MeasureOfAngle(AOB),45)",
"IsCentreOfCircle(O,O)"
],
"goal_cdl": "Value(LengthOfArc(OBA))"
} | As shown in the diagram, OA=3, ∠AOB=45°, the center of ⊙O is O. Find the length of ⌒OBA. | 如图所示，OA=3，∠AOB=45°，O是圆O的圆心。求弧OBA的长度。 | 3*pi/4 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [1.0, 0.0], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-0.5000000000000004, -0.8660254037844384], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [-1.8369701987210297e-16, -1.0], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [-0.8090169943749473, 0.5877852522924732], "D": [-0.8090169943749476, -0.587785252292473], "L": [-1.8369701987210297e-16, -1.0], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.8090169943749476, -0.587785252292473], "G": [0.30901699437494723, -0.9510565162951536], "H": [0.30901699437494723, -0.9510565162951536], "I": [-1.0, 1.2246467991473532e-16], "O": [-0.5000000000000004, -0.8660254037844384]}
shapes = [["O", "A", "O", "A", "B", "B", "O"], ["A", "O", "O", "B", "O", "B", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 34')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
35 | {
"construction_cdl": [
"Shape(QV,VS,SR,RQ)",
"Shape(VU,UT,TS,SV)",
"Collinear(QVU)",
"Collinear(RST)"
],
"text_cdl": [
"Equal(LengthOfLine(QR),2)",
"Equal(LengthOfLine(VS),7)",
"IsMidpointOfLine(S,RT)",
"IsMidpointOfLine(V,QU)",
"Trapezoid(QUTR)"
],
"image_cdl": [],
"goal_cdl": "Value(LengthOfLine(UT))"
} | As shown in the diagram, QR=2, VS=7, S is the midpoint of segment RT, V bisects segment QU, QU and TR are the non-parallel sides (legs) of trapezoid QUTR. Find the length of line UT. | 如图所示，QR=2，VS=7，S是线段RT的中点，V是线段QU的中点，QUTR是梯形。求直线UT的长度。 | 12 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.5000000000000001, 0.8660254037844386], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-1.0, 1.2246467991473532e-16], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [-0.8090169943749473, 0.5877852522924732], "D": [-0.8090169943749476, -0.587785252292473], "L": [-1.8369701987210297e-16, -1.0], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.8090169943749476, -0.587785252292473], "G": [0.30901699437494723, -0.9510565162951536], "H": [0.30901699437494723, -0.9510565162951536], "I": [-1.0, 1.2246467991473532e-16], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["Q", "V", "V", "S", "S", "R", "R", "Q"], ["V", "U", "U", "T", "T", "S", "S", "V"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 35')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
36 | {
"construction_cdl": [
"Shape(BAC,CB,BA)",
"Shape(BDA,AB,BD)",
"Shape(BCD,DB,BC)"
],
"text_cdl": [
"Equal(MeasureOfAngle(ABD),130)",
"Equal(MeasureOfAngle(CBA),x)",
"Equal(MeasureOfAngle(DBC),95)"
],
"image_cdl": [
"Equal(MeasureOfAngle(ABD),130)",
"Equal(MeasureOfAngle(CBA),x)",
"Equal(MeasureOfAngle(DBC),95)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, ∠ABD=130°, ∠CBA=x°, ∠DBC=95°. Find the value of x. | 如图所示，∠ABD=130°，∠CBA=x°，∠DBC=95°。求x的值。 | 135 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.5000000000000001, 0.8660254037844386], "S": [-0.4999999999999998, 0.8660254037844387], "T": [-1.0, 1.2246467991473532e-16], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.7071067811865474, -0.7071067811865477], "P": [0.5000000000000001, -0.8660254037844386], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0], "L": [-1.8369701987210297e-16, -1.0], "E": [0.30901699437494723, -0.9510565162951536], "F": [-0.8090169943749476, -0.587785252292473], "G": [0.30901699437494723, -0.9510565162951536], "H": [0.30901699437494723, -0.9510565162951536], "I": [-1.0, 1.2246467991473532e-16], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["B", "A", "C", "C", "B", "B", "A"], ["B", "D", "A", "A", "B", "B", "D"], ["B", "C", "D", "D", "B", "B", "C"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 36')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
37 | {
"construction_cdl": [
"Shape(HN,NK)",
"Shape(KN,NM)",
"Shape(NM,ME)",
"Shape(EM,ML)",
"Shape(ML,LC)",
"Shape(CL,LG)",
"Shape(GL,LI)",
"Shape(IL,LM)",
"Shape(LM,MD)",
"Shape(DM,MN)",
"Shape(MN,NS)",
"Shape(SN,NH)",
"Collinear(HNMLG)",
"Collinear(SNK)",
"Collinear(DME)",
"Collinear(ILC)"
],
"text_cdl": [
"Equal(MeasureOfAngle(DMN),56)",
"Equal(MeasureOfAngle(GLI),3*y-11)",
"Equal(MeasureOfAngle(HNK),4*x)",
"ParallelBetweenLine(LI,MD)",
"ParallelBetweenLine(MD,NS)"
],
"image_cdl": [
"Equal(MeasureOfAngle(DMN),56)",
"Equal(MeasureOfAngle(GLI),3*y-11)",
"Equal(MeasureOfAngle(HNK),4*x)",
"ParallelBetweenLine(LI,MD)",
"ParallelBetweenLine(MD,NS)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, ∠DMN=56°, ∠GLI=3*y-11°, ∠HNK=4*x°, LI is parallel to MD, MD is parallel to NS. Find the value of x. | 如图所示，∠DMN=56°，∠GLI=3*y-11°，∠HNK=4*x°，LI平行于MD，MD∥NS。求x的值。 | 31 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.5000000000000001, 0.8660254037844386], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.14231483827328523, -0.9898214418809327], "N": [0.41541501300188605, -0.9096319953545186], "P": [0.5000000000000001, -0.8660254037844386], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.9594929736144975, -0.2817325568414294], "W": [1.0, 0.0], "C": [1.0, 0.0], "D": [0.8412535328311812, 0.5406408174555976], "L": [-0.6548607339452852, -0.7557495743542582], "E": [0.41541501300188644, 0.9096319953545183], "F": [-0.8090169943749476, -0.587785252292473], "G": [-0.142314838273285, 0.9898214418809328], "H": [-0.654860733945285, 0.7557495743542583], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["H", "N", "N", "K"], ["K", "N", "N", "M"], ["N", "M", "M", "E"], ["E", "M", "M", "L"], ["M", "L", "L", "C"], ["C", "L", "L", "G"], ["G", "L", "L", "I"], ["I", "L", "L", "M"], ["L", "M", "M", "D"], ["D", "M", "M", "N"], ["M", "N", "N", "S"], ["S", "N", "N", "H"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 37')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
38 | {
"construction_cdl": [
"Shape(AC,CB,BA)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),8)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(BAC),60)",
"PerpendicularBetweenLine(AC,BC)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),8)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(BAC),60)",
"PerpendicularBetweenLine(AC,BC)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=y, AC=8, BC=x, ∠BAC=60°, AC is perpendicular to BC. Find the value of x. | 如图所示，AB=y，AC=8，BC=x，∠BAC=60°，AC垂直于BC。求x的值。 | 8*sqrt(3) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.5000000000000001, 0.8660254037844386], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [-0.14231483827328523, -0.9898214418809327], "N": [0.41541501300188605, -0.9096319953545186], "P": [0.5000000000000001, -0.8660254037844386], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.9594929736144975, -0.2817325568414294], "W": [1.0, 0.0], "C": [-0.5000000000000004, -0.8660254037844384], "D": [0.8412535328311812, 0.5406408174555976], "L": [-0.6548607339452852, -0.7557495743542582], "E": [0.41541501300188644, 0.9096319953545183], "F": [-0.8090169943749476, -0.587785252292473], "G": [-0.142314838273285, 0.9898214418809328], "H": [-0.654860733945285, 0.7557495743542583], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["A", "C", "C", "B", "B", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 38')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
39 | {
"construction_cdl": [
"Shape(JM,ME,EJ)",
"Shape(JE,EL,LK,KJ)",
"Collinear(MEL)"
],
"text_cdl": [
"Equal(LengthOfLine(EJ),6)",
"Equal(LengthOfLine(LK),7)",
"Equal(LengthOfLine(ML),4)",
"Parallelogram(JMLK)",
"PerpendicularBetweenLine(JE,LE)"
],
"image_cdl": [
"Equal(LengthOfLine(EJ),6)",
"Equal(LengthOfLine(LK),7)",
"Equal(LengthOfLine(ML),4)",
"PerpendicularBetweenLine(JE,LE)"
],
"goal_cdl": "Value(PerimeterOfQuadrilateral(JMLK))"
} | As shown in the diagram, EJ=6, LK=7, ML=4, quadrilateral JMLK is a parallelogram, JE is perpendicular to LE. Find the perimeter of quadrilateral JMLK. | 如图所示，EJ=6，LK=7，ML=4，JMLK是平行四边形，JE⊥LE。求JMLK的周长。 | 22 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.5000000000000001, 0.8660254037844386], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [6.123233995736766e-17, 1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [0.30901699437494723, -0.9510565162951536], "N": [0.41541501300188605, -0.9096319953545186], "P": [0.5000000000000001, -0.8660254037844386], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [0.30901699437494745, 0.9510565162951535], "K": [-0.8090169943749473, 0.5877852522924732], "W": [1.0, 0.0], "C": [-0.5000000000000004, -0.8660254037844384], "D": [0.8412535328311812, 0.5406408174555976], "L": [-0.8090169943749476, -0.587785252292473], "E": [1.0, 0.0], "F": [-0.8090169943749476, -0.587785252292473], "G": [-0.142314838273285, 0.9898214418809328], "H": [-0.654860733945285, 0.7557495743542583], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["J", "M", "M", "E", "E", "J"], ["J", "E", "E", "L", "L", "K", "K", "J"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 39')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
40 | {
"construction_cdl": [
"Shape(BA,AX,XB)",
"Shape(BX,XC,CB)",
"Collinear(AXC)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(AC),14)",
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BX),x)",
"PerpendicularBetweenLine(BX,CX)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(AC),14)",
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BX),x)",
"PerpendicularBetweenLine(BX,CX)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=8, AC=14, BC=8, BX=x, BX⊥CX. Find the value of x. | 如图所示，AB=8，AC=14，BC=8，BX=x，BX⊥CX。求x的值。 | sqrt(15) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.5000000000000001, 0.8660254037844386], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [0.30901699437494723, -0.9510565162951536], "N": [0.41541501300188605, -0.9096319953545186], "P": [0.5000000000000001, -0.8660254037844386], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.30901699437494745, 0.9510565162951535], "K": [-0.8090169943749473, 0.5877852522924732], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [0.8412535328311812, 0.5406408174555976], "L": [-0.8090169943749476, -0.587785252292473], "E": [1.0, 0.0], "F": [-0.8090169943749476, -0.587785252292473], "G": [-0.142314838273285, 0.9898214418809328], "H": [-0.654860733945285, 0.7557495743542583], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["B", "A", "A", "X", "X", "B"], ["B", "X", "X", "C", "C", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 40')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
41 | {
"construction_cdl": [
"Shape(LM,MN,NL)",
"Shape(LN,NP,PL)"
],
"text_cdl": [
"Equal(LengthOfLine(NM),4)",
"Equal(MeasureOfAngle(NLM),MeasureOfAngle(PLN))",
"Equal(MeasureOfAngle(PLN),25)",
"PerpendicularBetweenLine(LM,NM)",
"PerpendicularBetweenLine(NP,LP)"
],
"image_cdl": [
"Equal(LengthOfLine(NM),4)",
"Equal(MeasureOfAngle(NLM),MeasureOfAngle(PLN))",
"Equal(MeasureOfAngle(PLN),25)",
"PerpendicularBetweenLine(LM,NM)",
"PerpendicularBetweenLine(NP,LP)"
],
"goal_cdl": "Value(MeasureOfAngle(MNP))"
} | As shown in the diagram, NM=4, ∠NLM=∠PLN, ∠PLN=25°, LM⊥NM, NP⊥LP. Find the measure of ∠MNP. | 如图所示，NM=4，∠NLM=∠PLN，∠PLN=25°，LM⊥NM，NP⊥LP。求∠MNP的大小。 | 130 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.5000000000000001, 0.8660254037844386], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [6.123233995736766e-17, 1.0], "N": [-1.0, 1.2246467991473532e-16], "P": [-1.8369701987210297e-16, -1.0], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.30901699437494745, 0.9510565162951535], "K": [-0.8090169943749473, 0.5877852522924732], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [0.8412535328311812, 0.5406408174555976], "L": [1.0, 0.0], "E": [1.0, 0.0], "F": [-0.8090169943749476, -0.587785252292473], "G": [-0.142314838273285, 0.9898214418809328], "H": [-0.654860733945285, 0.7557495743542583], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["L", "M", "M", "N", "N", "L"], ["L", "N", "N", "P", "P", "L"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 41')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
42 | {
"construction_cdl": [
"Shape(HG,GJ,JH)",
"Shape(GF,FK,KJ,JG)",
"Collinear(HGF)",
"Collinear(KJH)"
],
"text_cdl": [
"Equal(LengthOfLine(GF),12)",
"Equal(LengthOfLine(HG),6)",
"Equal(LengthOfLine(HJ),8)",
"Equal(LengthOfLine(JK),x-4)",
"ParallelBetweenLine(GJ,FK)"
],
"image_cdl": [],
"goal_cdl": "Value(x)"
} | As shown in the diagram, GF=12, HG=6, HJ=8, JK=x-4, GJ is parallel to FK. Find the value of x. | 如图所示，GF=12，HG=6，HJ=8，JK=x-4，GJ∥FK。求x的值。 | 20 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.5000000000000001, 0.8660254037844386], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [6.123233995736766e-17, 1.0], "N": [-1.0, 1.2246467991473532e-16], "P": [-1.8369701987210297e-16, -1.0], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [-0.8090169943749476, -0.587785252292473], "K": [0.30901699437494723, -0.9510565162951536], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [0.8412535328311812, 0.5406408174555976], "L": [1.0, 0.0], "E": [1.0, 0.0], "F": [1.0, 0.0], "G": [0.30901699437494745, 0.9510565162951535], "H": [-0.8090169943749473, 0.5877852522924732], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["H", "G", "G", "J", "J", "H"], ["G", "F", "F", "K", "K", "J", "J", "G"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 42')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
43 | {
"construction_cdl": [
"Shape(NM,ML,LN)",
"Shape(LM,MR,RL)",
"Shape(NL,LQ,QN)",
"Shape(LR,RQ,QL)",
"Collinear(NLR)",
"Collinear(MLQ)"
],
"text_cdl": [
"Equal(LengthOfLine(ML),w)",
"Equal(LengthOfLine(MN),2*y+5)",
"Equal(LengthOfLine(MR),4*x-2)",
"Equal(LengthOfLine(QL),12)",
"Equal(LengthOfLine(QN),3*x+2)",
"Equal(LengthOfLine(QR),3*y)",
"Parallelogram(NMRQ)"
],
"image_cdl": [
"Equal(LengthOfLine(ML),w)",
"Equal(LengthOfLine(MN),2*y+5)",
"Equal(LengthOfLine(MR),4*x-2)",
"Equal(LengthOfLine(QL),12)",
"Equal(LengthOfLine(QN),3*x+2)",
"Equal(LengthOfLine(QR),3*y)"
],
"goal_cdl": "Value(w)"
} | As shown in the diagram, ML=w, MN=2*y+5, MR=4*x-2, QL=12, QN=3*x+2, QR=3*y, quadrilateral NMRQ is a ▱. Find the value of w. | 如图所示，ML=w，MN=2*y+5，MR=4*x-2，QL=12，QN=3*x+2，QR=3*y，NQ和MR是▱NMRQ的一组对边。求w的值。 | 12 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.30901699437494723, -0.9510565162951536], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [0.30901699437494745, 0.9510565162951535], "N": [-0.8090169943749473, 0.5877852522924732], "P": [-1.8369701987210297e-16, -1.0], "Q": [-0.8090169943749476, -0.587785252292473], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [-0.8090169943749476, -0.587785252292473], "K": [0.30901699437494723, -0.9510565162951536], "W": [1.0, 0.0], "C": [-1.0, 1.2246467991473532e-16], "D": [0.8412535328311812, 0.5406408174555976], "L": [1.0, 0.0], "E": [1.0, 0.0], "F": [1.0, 0.0], "G": [0.30901699437494745, 0.9510565162951535], "H": [-0.8090169943749473, 0.5877852522924732], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["N", "M", "M", "L", "L", "N"], ["L", "M", "M", "R", "R", "L"], ["N", "L", "L", "Q", "Q", "N"], ["L", "R", "R", "Q", "Q", "L"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 43')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
44 | {
"construction_cdl": [
"Shape(CB,BA,AC)"
],
"text_cdl": [
"Equal(LengthOfLine(BA),6)",
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CB),x)",
"Equal(MeasureOfAngle(BAC),45)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(AC,BC)"
],
"image_cdl": [
"Equal(LengthOfLine(BA),6)",
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CB),x)",
"Equal(MeasureOfAngle(BAC),45)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(AC,BC)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, BA=6, CA=x, CB=x, ∠BAC=45°, ∠CBA=45°, AC is perpendicular to BC. Find the value of x. | 如图所示，BA=6，CA=x，CB=x，∠BAC=45°，∠CBA=45°，AC⊥BC。求x的值。 | 3*sqrt(2) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.30901699437494723, -0.9510565162951536], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [-1.0, 1.2246467991473532e-16], "Z": [-1.8369701987210297e-16, -1.0], "M": [0.30901699437494745, 0.9510565162951535], "N": [-0.8090169943749473, 0.5877852522924732], "P": [-1.8369701987210297e-16, -1.0], "Q": [-0.8090169943749476, -0.587785252292473], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [-0.8090169943749476, -0.587785252292473], "K": [0.30901699437494723, -0.9510565162951536], "W": [1.0, 0.0], "C": [-0.5000000000000004, -0.8660254037844384], "D": [0.8412535328311812, 0.5406408174555976], "L": [1.0, 0.0], "E": [1.0, 0.0], "F": [1.0, 0.0], "G": [0.30901699437494745, 0.9510565162951535], "H": [-0.8090169943749473, 0.5877852522924732], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, -0.8660254037844386]}
shapes = [["C", "B", "B", "A", "A", "C"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 44')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
45 | {
"construction_cdl": [
"Shape(YV,VW,AYW)",
"Shape(AZY,YZ)",
"Shape(AYW,WX,AXZ,ZY)",
"Shape(AWX,XW)",
"Collinear(VYZ)",
"Collinear(VWX)",
"Cocircular(A,ZYWX)"
],
"text_cdl": [
"Equal(MeasureOfAngle(YVW),25)",
"Equal(MeasureOfArc(AXZ),110)",
"Equal(MeasureOfArc(AYW),x)"
],
"image_cdl": [
"Equal(MeasureOfAngle(YVW),25)",
"Equal(MeasureOfArc(AXZ),110)",
"Equal(MeasureOfArc(AYW),x)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, ∠YVW=25°, the measure of ⌒AXZ is 110, the measure of arc AYW is x. Find the value of x. | 如图所示，∠YVW=25°，⌒AXZ的角度为110，弧AYW的角度为x。求x的值。 | 60 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.30901699437494723, -0.9510565162951536], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.0, 1.2246467991473532e-16], "Y": [-0.5000000000000004, -0.8660254037844384], "Z": [0.5000000000000001, -0.8660254037844386], "M": [0.30901699437494745, 0.9510565162951535], "N": [-0.8090169943749473, 0.5877852522924732], "P": [-1.8369701987210297e-16, -1.0], "Q": [-0.8090169943749476, -0.587785252292473], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [-0.8090169943749476, -0.587785252292473], "K": [0.30901699437494723, -0.9510565162951536], "W": [-0.4999999999999998, 0.8660254037844387], "C": [-0.5000000000000004, -0.8660254037844384], "D": [0.8412535328311812, 0.5406408174555976], "L": [1.0, 0.0], "E": [1.0, 0.0], "F": [1.0, 0.0], "G": [0.30901699437494745, 0.9510565162951535], "H": [-0.8090169943749473, 0.5877852522924732], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["Y", "V", "V", "W", "A", "Y", "W"], ["A", "Z", "Y", "Y", "Z"], ["A", "Y", "W", "W", "X", "A", "X", "Z", "Z", "Y"], ["A", "W", "X", "X", "W"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 45')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
46 | {
"construction_cdl": [
"Shape(KJ,KJL,LK)",
"Shape(JK,KL,KLJ)",
"Cocircular(K,JL)"
],
"text_cdl": [
"Equal(LengthOfLine(KJ),11)",
"Equal(MeasureOfAngle(JKL),65)",
"IsCentreOfCircle(K,K)"
],
"image_cdl": [
"Equal(LengthOfLine(KJ),11)",
"Equal(MeasureOfAngle(JKL),65)",
"IsCentreOfCircle(K,K)"
],
"goal_cdl": "Value(AreaOfSector(KJL))"
} | As shown in the diagram, KJ=11, ∠JKL=65°, the center of circle K is K. Find the area of the sector KJL. | 如图所示，KJ=11，∠JKL=65°，圆K的圆心为K。求扇形KJL的面积。 | 7139*pi/72 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [0.30901699437494723, -0.9510565162951536], "S": [0.8412535328311812, -0.5406408174555974], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.0, 1.2246467991473532e-16], "Y": [-0.5000000000000004, -0.8660254037844384], "Z": [0.5000000000000001, -0.8660254037844386], "M": [0.30901699437494745, 0.9510565162951535], "N": [-0.8090169943749473, 0.5877852522924732], "P": [-1.8369701987210297e-16, -1.0], "Q": [-0.8090169943749476, -0.587785252292473], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.4999999999999998, 0.8660254037844387], "C": [-0.5000000000000004, -0.8660254037844384], "D": [0.8412535328311812, 0.5406408174555976], "L": [-0.5000000000000004, -0.8660254037844384], "E": [1.0, 0.0], "F": [1.0, 0.0], "G": [0.30901699437494745, 0.9510565162951535], "H": [-0.8090169943749473, 0.5877852522924732], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["K", "J", "K", "J", "L", "L", "K"], ["J", "K", "K", "L", "K", "L", "J"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 46')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
47 | {
"construction_cdl": [
"Shape(SP,PA,AS)",
"Shape(SA,AZ,ZR,RS)",
"Shape(RZ,ZQ,QR)",
"Collinear(PAZQ)"
],
"text_cdl": [
"Equal(LengthOfLine(AZ),y)",
"Equal(LengthOfLine(QZ),z)",
"Equal(LengthOfLine(RQ),12)",
"Equal(LengthOfLine(RS),10)",
"Equal(LengthOfLine(RZ),x)",
"Equal(MeasureOfAngle(SPA),45)",
"Equal(MeasureOfAngle(ZQR),30)",
"ParallelBetweenLine(SR,AZ)",
"PerpendicularBetweenLine(PA,SA)",
"PerpendicularBetweenLine(RZ,QZ)",
"Trapezoid(SPQR)"
],
"image_cdl": [
"Equal(LengthOfLine(AZ),y)",
"Equal(LengthOfLine(QZ),z)",
"Equal(LengthOfLine(RQ),12)",
"Equal(LengthOfLine(RS),10)",
"Equal(LengthOfLine(RZ),x)",
"Equal(MeasureOfAngle(SPA),45)",
"Equal(MeasureOfAngle(ZQR),30)",
"ParallelBetweenLine(SR,AZ)",
"PerpendicularBetweenLine(PA,SA)",
"PerpendicularBetweenLine(RZ,QZ)"
],
"goal_cdl": "Value(PerimeterOfQuadrilateral(SPQR))"
} | As shown in the diagram, AZ=y, QZ=z, RQ=12, RS=10, RZ=x, ∠SPA=45°, ∠ZQR=30°, SR is parallel to AZ, PA⊥SA, RZ is perpendicular to QZ, SPQR is a trapezoid. Find the perimeter of quadrilateral SPQR. | 如图所示，AZ=y，QZ=z，RQ=12，RS=10，RZ=x，∠SPA=45°，∠ZQR=30°，SR∥AZ，PA垂直于SA，RZ⊥QZ，四边形SPQR是梯形。求SPQR的周长。 | 6*sqrt(2)+6*sqrt(3)+38 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.0, 1.2246467991473532e-16], "Y": [-0.5000000000000004, -0.8660254037844384], "Z": [0.5000000000000001, -0.8660254037844386], "M": [0.30901699437494745, 0.9510565162951535], "N": [-0.8090169943749473, 0.5877852522924732], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.4999999999999998, 0.8660254037844387], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.4999999999999998, 0.8660254037844387], "C": [-0.5000000000000004, -0.8660254037844384], "D": [0.8412535328311812, 0.5406408174555976], "L": [-0.5000000000000004, -0.8660254037844384], "E": [1.0, 0.0], "F": [1.0, 0.0], "G": [0.30901699437494745, 0.9510565162951535], "H": [-0.8090169943749473, 0.5877852522924732], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["S", "P", "P", "A", "A", "S"], ["S", "A", "A", "Z", "Z", "R", "R", "S"], ["R", "Z", "Z", "Q", "Q", "R"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 47')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
48 | {
"construction_cdl": [
"Shape(EY,YQ,QF,FE)",
"Shape(YM,MA,AQ,QY)",
"Collinear(EYM)",
"Collinear(FQA)"
],
"text_cdl": [
"Equal(MeasureOfAngle(EYQ),3*y+1)",
"Equal(MeasureOfAngle(MAQ),3*x+11)",
"Equal(MeasureOfAngle(YQF),4*x-5)",
"ParallelBetweenLine(EF,YQ)",
"ParallelBetweenLine(QA,YM)",
"ParallelBetweenLine(YQ,MA)"
],
"image_cdl": [
"Equal(MeasureOfAngle(EYQ),3*y+1)",
"Equal(MeasureOfAngle(MAQ),3*x+11)",
"Equal(MeasureOfAngle(YQF),4*x-5)",
"ParallelBetweenLine(EF,YQ)",
"ParallelBetweenLine(QA,YM)",
"ParallelBetweenLine(YQ,MA)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, ∠EYQ=3*y+1°, ∠MAQ=3*x+11°, ∠YQF=4*x-5°, EF∥YQ, QA is parallel to YM, YQ∥MA. Find the value of y. | 如图所示，∠EYQ=3*y+1°，∠MAQ=3*x+11°，∠YQF=4*x-5°，EF平行于YQ，QA∥YM，YQ平行于MA。求y的值。 | 40 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.0, 1.2246467991473532e-16], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.5000000000000001, -0.8660254037844386], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8090169943749473, 0.5877852522924732], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.4999999999999998, 0.8660254037844387], "C": [-0.5000000000000004, -0.8660254037844384], "D": [0.8412535328311812, 0.5406408174555976], "L": [-0.5000000000000004, -0.8660254037844384], "E": [0.5000000000000001, 0.8660254037844386], "F": [-0.4999999999999998, 0.8660254037844387], "G": [0.30901699437494745, 0.9510565162951535], "H": [-0.8090169943749473, 0.5877852522924732], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["E", "Y", "Y", "Q", "Q", "F", "F", "E"], ["Y", "M", "M", "A", "A", "Q", "Q", "Y"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 48')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
49 | {
"construction_cdl": [
"Shape(XW,WA,AX)",
"Shape(AW,WZ,ZA)",
"Shape(AZ,ZY,YA)",
"Shape(XA,AY,YX)",
"Collinear(XAZ)",
"Collinear(WAY)"
],
"text_cdl": [
"Equal(MeasureOfAngle(AXW),82)",
"Equal(MeasureOfAngle(YXA),33)",
"Parallelogram(XWZY)"
],
"image_cdl": [
"Equal(MeasureOfAngle(AXW),82)",
"Equal(MeasureOfAngle(YXA),33)"
],
"goal_cdl": "Value(MeasureOfAngle(WZY))"
} | As shown in the diagram, ∠AXW=82°, ∠YXA=33°, quadrilateral XWZY is a ▱. Find the measure of ∠WZY. | 如图所示，∠AXW=82°，∠YXA=33°，WX和ZY是平行四边形XWZY的一组对边。求∠WZY的大小。 | 115 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-0.8090169943749473, 0.5877852522924732], "Y": [-0.8090169943749476, -0.587785252292473], "Z": [0.30901699437494723, -0.9510565162951536], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8090169943749473, 0.5877852522924732], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [0.30901699437494745, 0.9510565162951535], "C": [-0.5000000000000004, -0.8660254037844384], "D": [0.8412535328311812, 0.5406408174555976], "L": [-0.5000000000000004, -0.8660254037844384], "E": [0.5000000000000001, 0.8660254037844386], "F": [-0.4999999999999998, 0.8660254037844387], "G": [0.30901699437494745, 0.9510565162951535], "H": [-0.8090169943749473, 0.5877852522924732], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["X", "W", "W", "A", "A", "X"], ["A", "W", "W", "Z", "Z", "A"], ["A", "Z", "Z", "Y", "Y", "A"], ["X", "A", "A", "Y", "Y", "X"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 49')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
50 | {
"construction_cdl": [
"Shape(DE,EF,FD)",
"Shape(CD,DF,FG,GC)",
"Shape(GF,FH,HG)",
"Collinear(CDE)",
"Collinear(EFH)",
"Collinear(HGC)"
],
"text_cdl": [
"Equal(LengthOfLine(FE),6)",
"Equal(LengthOfLine(FG),3)",
"Equal(LengthOfLine(FH),4)",
"Equal(LengthOfLine(HG),2)",
"SimilarBetweenTriangle(DEF,GFH)"
],
"image_cdl": [
"Equal(LengthOfLine(FE),6)",
"Equal(LengthOfLine(FG),3)",
"Equal(LengthOfLine(FH),4)",
"Equal(LengthOfLine(HG),2)"
],
"goal_cdl": "Value(PerimeterOfTriangle(DEF))"
} | As shown in the diagram, FE=6, FG=3, FH=4, HG=2, triangle DEF is similar to triangle GFH.. Find the perimeter of △DEF. | 如图所示，FE=6，FG=3，FH=4，HG=2，△DEF相似于△GFH。求△DEF的周长。 | 27/2 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-0.8090169943749473, 0.5877852522924732], "Y": [-0.8090169943749476, -0.587785252292473], "Z": [0.30901699437494723, -0.9510565162951536], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8090169943749473, 0.5877852522924732], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [0.30901699437494745, 0.9510565162951535], "C": [1.0, 0.0], "D": [0.5000000000000001, 0.8660254037844386], "L": [-0.5000000000000004, -0.8660254037844384], "E": [-0.4999999999999998, 0.8660254037844387], "F": [-1.0, 1.2246467991473532e-16], "G": [-0.5000000000000004, -0.8660254037844384], "H": [0.5000000000000001, -0.8660254037844386], "I": [-0.9594929736144974, 0.28173255684142967], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["D", "E", "E", "F", "F", "D"], ["C", "D", "D", "F", "F", "G", "G", "C"], ["G", "F", "F", "H", "H", "G"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 50')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
51 | {
"construction_cdl": [
"Shape(GW,WL)",
"Shape(LW,WX)",
"Shape(WX,XE)",
"Shape(EX,XN)",
"Shape(NX,XZ)",
"Shape(XZ,ZK)",
"Shape(KZ,ZH)",
"Shape(HZ,ZY)",
"Shape(ZY,YM)",
"Shape(MY,YI)",
"Shape(IY,YW)",
"Shape(YW,WG)",
"Shape(WY,YZ,ZX,XW)",
"Collinear(GWXN)",
"Collinear(IYZK)",
"Collinear(LWYM)",
"Collinear(EXZH)"
],
"text_cdl": [
"Equal(MeasureOfAngle(LWX),3*a+40)",
"Equal(MeasureOfAngle(WXE),2*a+25)",
"Equal(MeasureOfAngle(XZK),5*b-26)",
"ParallelBetweenLine(WL,XE)",
"ParallelBetweenLine(XN,ZK)"
],
"image_cdl": [
"ParallelBetweenLine(WL,XE)",
"ParallelBetweenLine(XN,ZK)"
],
"goal_cdl": "Value(a)"
} | As shown in the diagram, ∠LWX=3*a+40°, ∠WXE=2*a+25°, ∠XZK=5*b-26°, WL∥XE, XN is parallel to ZK. Find the value of a. | 如图所示，∠LWX=3*a+40°，∠WXE=2*a+25°，∠XZK=5*b-26°，WL∥XE，XN平行于ZK。求a的值。 | 23 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [1.0, 0.0], "D": [0.5000000000000001, 0.8660254037844386], "L": [-0.8660254037844387, 0.49999999999999994], "E": [1.0, 0.0], "F": [-1.0, 1.2246467991473532e-16], "G": [0.8660254037844387, 0.49999999999999994], "H": [0.5000000000000001, 0.8660254037844386], "I": [6.123233995736766e-17, 1.0], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["G", "W", "W", "L"], ["L", "W", "W", "X"], ["W", "X", "X", "E"], ["E", "X", "X", "N"], ["N", "X", "X", "Z"], ["X", "Z", "Z", "K"], ["K", "Z", "Z", "H"], ["H", "Z", "Z", "Y"], ["Z", "Y", "Y", "M"], ["M", "Y", "Y", "I"], ["I", "Y", "Y", "W"], ["Y", "W", "W", "G"], ["W", "Y", "Y", "Z", "Z", "X", "X", "W"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 51')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
52 | {
"construction_cdl": [
"Shape(DG,GF,FD)",
"Shape(FG,GA,AF)",
"Shape(BG,GC,CB)",
"Shape(AB,BC,CA)",
"Collinear(DFA)",
"Collinear(ABG)"
],
"text_cdl": [
"Equal(MeasureOfAngle(AGC),40)",
"Equal(MeasureOfAngle(DGF),53)",
"PerpendicularBetweenLine(CB,GB)",
"PerpendicularBetweenLine(FG,CG)",
"PerpendicularBetweenLine(GF,DF)"
],
"image_cdl": [
"PerpendicularBetweenLine(CB,GB)",
"PerpendicularBetweenLine(FG,CG)",
"PerpendicularBetweenLine(GF,DF)"
],
"goal_cdl": "Value(MeasureOfAngle(FDG))"
} | As shown in the diagram, ∠AGC=40°, ∠DGF=53°, CB⊥GB, FG is perpendicular to CG, GF is perpendicular to DF. Find the measure of ∠FDG. | 如图所示，∠AGC=40°，∠DGF=53°，CB垂直于GB，FG垂直于CG，GF⊥DF。求∠FDG的大小。 | 37 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.5000000000000001, 0.8660254037844386], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.4999999999999998, 0.8660254037844387], "D": [-1.0, 1.2246467991473532e-16], "L": [-0.8660254037844387, 0.49999999999999994], "E": [1.0, 0.0], "F": [-0.5000000000000004, -0.8660254037844384], "G": [0.5000000000000001, -0.8660254037844386], "H": [0.5000000000000001, 0.8660254037844386], "I": [6.123233995736766e-17, 1.0], "O": [-0.5000000000000004, -0.8660254037844384], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["D", "G", "G", "F", "F", "D"], ["F", "G", "G", "A", "A", "F"], ["B", "G", "G", "C", "C", "B"], ["A", "B", "B", "C", "C", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 52')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
53 | {
"construction_cdl": [
"Shape(OE,OEF,FO)",
"Shape(OF,OFA,AO)",
"Shape(OA,OAC,CO)",
"Shape(OC,OCB,BO)",
"Shape(OB,OBE,EO)",
"Collinear(EOC)",
"Collinear(AOB)",
"Cocircular(O,EFACB)"
],
"text_cdl": [
"Equal(MeasureOfAngle(FOE),45)",
"IsCentreOfCircle(O,O)",
"PerpendicularBetweenLine(CO,AO)",
"PerpendicularBetweenLine(EO,BO)"
],
"image_cdl": [
"Equal(MeasureOfAngle(FOE),45)",
"IsCentreOfCircle(O,O)",
"PerpendicularBetweenLine(CO,AO)",
"PerpendicularBetweenLine(EO,BO)"
],
"goal_cdl": "Value(MeasureOfArc(OAE))"
} | As shown in the diagram, ∠FOE=45°, the center of circle O is O, CO⊥AO, EO⊥BO. Find the measure of arc OAE. | 如图所示，∠FOE=45°，O是⊙O的圆心，CO⊥AO，EO垂直于BO。求弧OAE的角度。 | 270 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.5000000000000001, 0.8660254037844386], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.4999999999999998, 0.8660254037844387], "D": [-1.0, 1.2246467991473532e-16], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.5000000000000004, -0.8660254037844384], "G": [0.5000000000000001, -0.8660254037844386], "H": [0.5000000000000001, 0.8660254037844386], "I": [6.123233995736766e-17, 1.0], "O": [0.5000000000000001, -0.8660254037844386], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["O", "E", "O", "E", "F", "F", "O"], ["O", "F", "O", "F", "A", "A", "O"], ["O", "A", "O", "A", "C", "C", "O"], ["O", "C", "O", "C", "B", "B", "O"], ["O", "B", "O", "B", "E", "E", "O"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 53')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
54 | {
"construction_cdl": [
"Shape(DC,CB,BH,ODH)",
"Shape(OD,ODH,HO)",
"Collinear(DOH)",
"Cocircular(O,DH)"
],
"text_cdl": [
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BH),12)",
"IsCentreOfCircle(O,O)",
"Rectangle(DCBH)"
],
"image_cdl": [
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BH),12)",
"IsCentreOfCircle(O,O)"
],
"goal_cdl": "Value(Sub(AreaOfQuadrilateral(DCBH),AreaOfSector(ODH)))"
} | As shown in the diagram, BC=8, BH=12, the center of circle O is O, quadrilateral DCBH is a rectangle. Find the area of quadrilateral DCBH minus the area of the sector ODH. | 如图所示，BC=8，BH=12，圆O的圆心为O，四边形DCBH是矩形。求四边形DCBH的面积减去扇形ODH的面积。 | 96-8*pi | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [1.0, 0.0], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [0.30901699437494745, 0.9510565162951535], "D": [-0.8090169943749473, 0.5877852522924732], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.5000000000000004, -0.8660254037844384], "G": [0.5000000000000001, -0.8660254037844386], "H": [-0.8090169943749476, -0.587785252292473], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["D", "C", "C", "B", "B", "H", "O", "D", "H"], ["O", "D", "O", "D", "H", "H", "O"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 54')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
55 | {
"construction_cdl": [
"Shape(AC,CB,BA)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),6)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(AC,BC)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),6)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(AC,BC)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=10, AC=6, BC=x, AC⊥BC. Find the value of x. | 如图所示，AB=10，AC=6，BC=x，AC垂直于BC。求x的值。 | 8 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.5000000000000001, 0.8660254037844386], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.5000000000000004, -0.8660254037844384], "D": [-0.8090169943749473, 0.5877852522924732], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.5000000000000004, -0.8660254037844384], "G": [0.5000000000000001, -0.8660254037844386], "H": [-0.8090169943749476, -0.587785252292473], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["A", "C", "C", "B", "B", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 55')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
56 | {
"construction_cdl": [
"Shape(AF,FP,PA)",
"Shape(FE,EP,PF)",
"Shape(AP,PB,BA)",
"Shape(PE,ED,DP)",
"Shape(PD,DC,CP)",
"Shape(BP,PC,CB)",
"Collinear(AFE)",
"Collinear(EDC)",
"Collinear(CBA)",
"Collinear(EPB)",
"Collinear(FPC)",
"Collinear(DPA)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),10.9)",
"Equal(LengthOfLine(EP),14.9)",
"Equal(LengthOfLine(PA),13)",
"Equal(MeasureOfAngle(DCP),28.5)",
"Equal(MeasureOfAngle(PAE),33)",
"IsIncenterOfTriangle(P,AEC)",
"PerpendicularBetweenLine(ED,PD)",
"PerpendicularBetweenLine(PB,AB)",
"PerpendicularBetweenLine(PF,EF)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),10.9)",
"Equal(LengthOfLine(EP),14.9)",
"Equal(LengthOfLine(PA),13)",
"Equal(MeasureOfAngle(DCP),28.5)",
"Equal(MeasureOfAngle(PAE),33)",
"PerpendicularBetweenLine(ED,PD)",
"PerpendicularBetweenLine(PB,AB)",
"PerpendicularBetweenLine(PF,EF)"
],
"goal_cdl": "Value(MeasureOfAngle(CAD))"
} | As shown in the diagram, AB=10.9, EP=14.9, PA=13, ∠DCP=28.5°, ∠PAE=33°, P is the center of the inscribed circle of triangle AEC, ED is perpendicular to PD, PB is perpendicular to AB, PF is perpendicular to EF. Find the measure of ∠CAD. | 如图所示，AB=10.9，EP=14.9，PA=13，∠DCP=28.5°，∠PAE=33°，P是三角形AEC内切圆的圆心，ED垂直于PD，PB垂直于AB，PF⊥EF。求∠CAD的大小。 | 33 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.6234898018587334, -0.7818314824680299], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.6234898018587336, 0.7818314824680298], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.22252093395631434, 0.9749279121818236], "D": [-0.900968867902419, 0.43388373911755823], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-0.9009688679024191, -0.433883739117558], "F": [-0.2225209339563146, -0.9749279121818236], "G": [0.5000000000000001, -0.8660254037844386], "H": [-0.8090169943749476, -0.587785252292473], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["A", "F", "F", "P", "P", "A"], ["F", "E", "E", "P", "P", "F"], ["A", "P", "P", "B", "B", "A"], ["P", "E", "E", "D", "D", "P"], ["P", "D", "D", "C", "C", "P"], ["B", "P", "P", "C", "C", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 56')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
57 | {
"construction_cdl": [
"Shape(AD,DP,PA)",
"Shape(PD,DC,CP)",
"Shape(PC,CB,BP)",
"Shape(AP,PB,BA)",
"Collinear(APC)",
"Collinear(DPB)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),14)",
"PerpendicularBetweenLine(DP,AP)",
"Rhombus(ADCB)"
],
"image_cdl": [
"PerpendicularBetweenLine(DP,AP)"
],
"goal_cdl": "Value(LengthOfLine(BC))"
} | As shown in the diagram, AB=14, DP is perpendicular to AP, ADCB is a rhombus. Find the length of line BC. | 如图所示，AB=14，DP⊥AP，四边形ADCB是菱形。求直线BC的长度。 | 14 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.30901699437494745, 0.9510565162951535], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.8090169943749473, 0.5877852522924732], "D": [-0.8090169943749476, -0.587785252292473], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-0.9009688679024191, -0.433883739117558], "F": [-0.2225209339563146, -0.9749279121818236], "G": [0.5000000000000001, -0.8660254037844386], "H": [-0.8090169943749476, -0.587785252292473], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["A", "D", "D", "P", "P", "A"], ["P", "D", "D", "C", "C", "P"], ["P", "C", "C", "B", "B", "P"], ["A", "P", "P", "B", "B", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 57')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
58 | {
"construction_cdl": [
"Shape(FB,BE,EF)",
"Shape(DE,EA,AD)",
"Shape(BC,CE,EB)",
"Shape(FE,ED)",
"Shape(FE,EA)",
"Shape(DA,AG)",
"Shape(AE,EC)",
"Collinear(BEAG)",
"Collinear(FEC)"
],
"text_cdl": [
"Equal(MeasureOfAngle(BCE),MeasureOfAngle(EBC))",
"Equal(MeasureOfAngle(DAG),136)",
"Equal(MeasureOfAngle(DEA),47)",
"Equal(MeasureOfAngle(EFB),63)",
"Equal(MeasureOfAngle(FED),69)"
],
"image_cdl": [
"Equal(MeasureOfAngle(DAG),136)",
"Equal(MeasureOfAngle(DEA),47)",
"Equal(MeasureOfAngle(EFB),63)",
"Equal(MeasureOfAngle(FED),69)"
],
"goal_cdl": "Value(MeasureOfAngle(EBC))"
} | As shown in the diagram, ∠BCE=∠EBC, ∠DAG=136°, ∠DEA=47°, ∠EFB=63°, ∠FED=69°. Find the measure of ∠EBC. | 如图所示，∠BCE=∠EBC，∠DAG=136°，∠DEA=47°，∠EFB=63°，∠FED=69°。求∠EBC的大小。 | 32 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.6234898018587336, 0.7818314824680298], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.22252093395631434, 0.9749279121818236], "D": [-0.900968867902419, 0.43388373911755823], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-0.9009688679024191, -0.433883739117558], "F": [-0.2225209339563146, -0.9749279121818236], "G": [0.6234898018587334, -0.7818314824680299], "H": [-0.8090169943749476, -0.587785252292473], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["F", "B", "B", "E", "E", "F"], ["D", "E", "E", "A", "A", "D"], ["B", "C", "C", "E", "E", "B"], ["F", "E", "E", "D"], ["F", "E", "E", "A"], ["D", "A", "A", "G"], ["A", "E", "E", "C"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 58')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
59 | {
"construction_cdl": [
"Shape(GW,WL)",
"Shape(LW,WX)",
"Shape(WX,XE)",
"Shape(EX,XN)",
"Shape(NX,XZ)",
"Shape(XZ,ZK)",
"Shape(KZ,ZH)",
"Shape(HZ,ZY)",
"Shape(ZY,YM)",
"Shape(MY,YI)",
"Shape(IY,YW)",
"Shape(YW,WG)",
"Shape(WY,YZ,ZX,XW)",
"Collinear(GWXN)",
"Collinear(IYZK)",
"Collinear(LWYM)",
"Collinear(EXZH)"
],
"text_cdl": [
"Equal(MeasureOfAngle(LWX),53)",
"ParallelBetweenLine(WL,XE)",
"ParallelBetweenLine(XN,ZK)"
],
"image_cdl": [
"ParallelBetweenLine(WL,XE)",
"ParallelBetweenLine(XN,ZK)"
],
"goal_cdl": "Value(MeasureOfAngle(XZK))"
} | As shown in the diagram, ∠LWX=53°, WL∥XE, XN is parallel to ZK. Find the measure of ∠XZK. | 如图所示，∠LWX=53°，WL∥XE，XN平行于ZK。求∠XZK的大小。 | 53 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.6234898018587336, 0.7818314824680298], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.22252093395631434, 0.9749279121818236], "D": [-0.900968867902419, 0.43388373911755823], "L": [-0.8660254037844387, 0.49999999999999994], "E": [1.0, 0.0], "F": [-0.2225209339563146, -0.9749279121818236], "G": [0.8660254037844387, 0.49999999999999994], "H": [0.5000000000000001, 0.8660254037844386], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["G", "W", "W", "L"], ["L", "W", "W", "X"], ["W", "X", "X", "E"], ["E", "X", "X", "N"], ["N", "X", "X", "Z"], ["X", "Z", "Z", "K"], ["K", "Z", "Z", "H"], ["H", "Z", "Z", "Y"], ["Z", "Y", "Y", "M"], ["M", "Y", "Y", "I"], ["I", "Y", "Y", "W"], ["Y", "W", "W", "G"], ["W", "Y", "Y", "Z", "Z", "X", "X", "W"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 59')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
60 | {
"construction_cdl": [
"Shape(AC,CD,DA)",
"Shape(DC,CB,BD)",
"Collinear(BDA)"
],
"text_cdl": [
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(AD),4)",
"Equal(LengthOfLine(BC),y)",
"Equal(LengthOfLine(BD),9)",
"Equal(LengthOfLine(CD),z)",
"PerpendicularBetweenLine(AC,BC)",
"PerpendicularBetweenLine(BD,CD)"
],
"image_cdl": [
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(AD),4)",
"Equal(LengthOfLine(BC),y)",
"Equal(LengthOfLine(BD),9)",
"Equal(LengthOfLine(CD),z)",
"PerpendicularBetweenLine(AC,BC)",
"PerpendicularBetweenLine(BD,CD)"
],
"goal_cdl": "Value(z)"
} | As shown in the diagram, AC=x, AD=4, BC=y, BD=9, CD=z, AC⊥BC, BD⊥CD. Find the value of z. | 如图所示，AC=x，AD=4，BC=y，BD=9，CD=z，AC⊥BC，BD⊥CD。求z的值。 | 6 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.8660254037844387, 0.49999999999999994], "E": [1.0, 0.0], "F": [-0.2225209339563146, -0.9749279121818236], "G": [0.8660254037844387, 0.49999999999999994], "H": [0.5000000000000001, 0.8660254037844386], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["A", "C", "C", "D", "D", "A"], ["D", "C", "C", "B", "B", "D"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 60')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
61 | {
"construction_cdl": [
"Shape(AC,CB,BA)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(CA),10)",
"Equal(LengthOfLine(CB),a)",
"Equal(MeasureOfAngle(BAC),60)"
],
"image_cdl": [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(CA),10)",
"Equal(LengthOfLine(CB),a)",
"Equal(MeasureOfAngle(BAC),60)"
],
"goal_cdl": "Value(a)"
} | As shown in the diagram, AB=8, CA=10, CB=a, ∠BAC=60°. Find the value of a. | 如图所示，AB=8，CA=10，CB=a，∠BAC=60°。求a的值。 | 2*sqrt(21) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [-0.4999999999999998, 0.8660254037844387], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.5000000000000004, -0.8660254037844384], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.8660254037844387, 0.49999999999999994], "E": [1.0, 0.0], "F": [-0.2225209339563146, -0.9749279121818236], "G": [0.8660254037844387, 0.49999999999999994], "H": [0.5000000000000001, 0.8660254037844386], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["A", "C", "C", "B", "B", "A"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 61')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
62 | {
"construction_cdl": [
"Shape(DB,FBA,AD)",
"Shape(BD,DF,FB)",
"Shape(BF,FE,EB)",
"Shape(FD,DA,FAC,CE,EF)",
"Shape(BE,EC,FCB)",
"Collinear(BEC)",
"Collinear(BDA)",
"Cocircular(F,BAC)"
],
"text_cdl": [
"Equal(LengthOfLine(AB),LengthOfLine(BC))",
"Equal(LengthOfLine(DF),3*x-7)",
"Equal(LengthOfLine(FE),x+9)",
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(CE,FE)",
"PerpendicularBetweenLine(FD,AD)"
],
"image_cdl": [
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(CE,FE)",
"PerpendicularBetweenLine(FD,AD)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, AB=BC, DF=3*x-7, FE=x+9, the center of ⊙F is F, CE is perpendicular to FE, FD⊥AD. Find the value of x. | 如图所示，AB=BC，DF=3*x-7，FE=x+9，圆F的圆心为F，CE垂直于FE，FD垂直于AD。求x的值。 | 8 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.5000000000000001, 0.8660254037844386], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.4999999999999998, 0.8660254037844387], "D": [-1.0, 1.2246467991473532e-16], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-0.5000000000000004, -0.8660254037844384], "F": [0.5000000000000001, -0.8660254037844386], "G": [0.8660254037844387, 0.49999999999999994], "H": [0.5000000000000001, 0.8660254037844386], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["D", "B", "F", "B", "A", "A", "D"], ["B", "D", "D", "F", "F", "B"], ["B", "F", "F", "E", "E", "B"], ["F", "D", "D", "A", "F", "A", "C", "C", "E", "E", "F"], ["B", "E", "E", "C", "F", "C", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 62')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
63 | {
"construction_cdl": [
"Shape(EC,CF,FD,DE)"
],
"text_cdl": [
"Equal(MeasureOfAngle(CFD),x+36)",
"Equal(MeasureOfAngle(DEC),2*y)",
"Equal(MeasureOfAngle(ECF),78)",
"Equal(MeasureOfAngle(FDE),110)",
"ParallelBetweenLine(CE,FD)"
],
"image_cdl": [
"Equal(MeasureOfAngle(CFD),x+36)",
"Equal(MeasureOfAngle(DEC),2*y)",
"Equal(MeasureOfAngle(ECF),78)",
"Equal(MeasureOfAngle(FDE),110)",
"ParallelBetweenLine(CE,FD)"
],
"goal_cdl": "Value(y)"
} | As shown in the diagram, ∠CFD=x+36°, ∠DEC=2*y°, ∠ECF=78°, ∠FDE=110°, CE is parallel to FD. Find the value of y. | 如图所示，∠CFD=x+36°，∠DEC=2*y°，∠ECF=78°，∠FDE=110°，CE平行于FD。求y的值。 | 35 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.5000000000000001, 0.8660254037844386], "J": [1.0, 0.0], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [1.0, 0.0], "D": [6.123233995736766e-17, 1.0], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-1.8369701987210297e-16, -1.0], "G": [0.8660254037844387, 0.49999999999999994], "H": [0.5000000000000001, 0.8660254037844386], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["E", "C", "C", "F", "F", "D", "D", "E"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 63')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
64 | {
"construction_cdl": [
"Shape(AGF,FB,BG)",
"Shape(AB,BF,AFJ,JA)",
"Shape(BA,AJ,JH,HB)",
"Shape(AJH,HJ)",
"Shape(BH,HG,GB)",
"Shape(AHG,GH)",
"Collinear(FBH)",
"Collinear(GBAJ)",
"Cocircular(A,GFJH)"
],
"text_cdl": [
"Equal(MeasureOfAngle(AJH),x)",
"Equal(MeasureOfAngle(HGB),2*x)",
"PerpendicularBetweenLine(GB,HB)",
"PerpendicularBetweenLine(JH,GH)"
],
"image_cdl": [
"PerpendicularBetweenLine(GB,HB)",
"PerpendicularBetweenLine(JH,GH)"
],
"goal_cdl": "Value(MeasureOfAngle(BHG))"
} | As shown in the diagram, ∠AJH=x°, ∠HGB=2*x°, GB⊥HB, JH is perpendicular to GH. Find the measure of ∠BHG. | 如图所示，∠AJH=x°，∠HGB=2*x°，GB垂直于HB，JH⊥GH。求∠BHG的大小。 | 30 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.5000000000000001, 0.8660254037844386], "J": [0.5000000000000001, -0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [1.0, 0.0], "D": [6.123233995736766e-17, 1.0], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.4999999999999998, 0.8660254037844387], "G": [-1.0, 1.2246467991473532e-16], "H": [-0.5000000000000004, -0.8660254037844384], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["A", "G", "F", "F", "B", "B", "G"], ["A", "B", "B", "F", "A", "F", "J", "J", "A"], ["B", "A", "A", "J", "J", "H", "H", "B"], ["A", "J", "H", "H", "J"], ["B", "H", "H", "G", "G", "B"], ["A", "H", "G", "G", "H"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 64')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
65 | {
"construction_cdl": [
"Shape(BC,BCA,AB)",
"Shape(BA,BAG,GB)",
"Shape(BG,BGF,FB)",
"Shape(BF,BFD,DB)",
"Shape(BD,BDC,CB)",
"Collinear(CBG)",
"Collinear(ABD)",
"Cocircular(B,AGFDC)"
],
"text_cdl": [
"Equal(MeasureOfAngle(CBD),55)",
"Equal(MeasureOfAngle(FBG),35)",
"IsCentreOfCircle(B,B)"
],
"image_cdl": [
"Equal(MeasureOfAngle(CBD),55)",
"Equal(MeasureOfAngle(FBG),35)",
"IsCentreOfCircle(B,B)"
],
"goal_cdl": "Value(MeasureOfArc(BCD))"
} | As shown in the diagram, ∠CBD=55°, ∠FBG=35°, B is the center of circle B. Find the measure of arc BCD. | 如图所示，∠CBD=55°，∠FBG=35°，圆B的圆心为B。求⌒BCD的角度。 | 305 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [0.5000000000000001, 0.8660254037844386], "J": [0.5000000000000001, -0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-0.4999999999999998, 0.8660254037844387], "D": [-1.0, 1.2246467991473532e-16], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.5000000000000004, -0.8660254037844384], "G": [0.5000000000000001, -0.8660254037844386], "H": [-0.5000000000000004, -0.8660254037844384], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["B", "C", "B", "C", "A", "A", "B"], ["B", "A", "B", "A", "G", "G", "B"], ["B", "G", "B", "G", "F", "F", "B"], ["B", "F", "B", "F", "D", "D", "B"], ["B", "D", "B", "D", "C", "C", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 65')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
66 | {
"construction_cdl": [
"Shape(BC,CD,DB)",
"Shape(BD,DA,AB)"
],
"text_cdl": [
"Equal(LengthOfLine(BA),3*x-13)",
"Equal(LengthOfLine(BC),2*x+5)",
"Equal(MeasureOfAngle(BCD),MeasureOfAngle(CDB))",
"Equal(MeasureOfAngle(BDA),MeasureOfAngle(DAB))",
"Equal(MeasureOfAngle(DBC),60)"
],
"image_cdl": [
"Equal(LengthOfLine(BA),3*x-13)",
"Equal(LengthOfLine(BC),2*x+5)",
"Equal(MeasureOfAngle(BCD),MeasureOfAngle(CDB))",
"Equal(MeasureOfAngle(BDA),MeasureOfAngle(DAB))",
"Equal(MeasureOfAngle(DBC),60)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, BA=3*x-13, BC=2*x+5, ∠BCD=∠CDB, ∠BDA=∠DAB, ∠DBC=60°. Find the value of x. | 如图所示，BA=3*x-13，BC=2*x+5，∠BCD=∠CDB，∠BDA=∠DAB，∠DBC=60°。求x的值。 | 18 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [-1.0, 1.2246467991473532e-16], "S": [-0.5000000000000004, -0.8660254037844384], "T": [-1.0, 1.2246467991473532e-16], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [-0.5000000000000004, -0.8660254037844384], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.5000000000000001, -0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.5000000000000004, -0.8660254037844384], "G": [0.5000000000000001, -0.8660254037844386], "H": [-0.5000000000000004, -0.8660254037844384], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["B", "C", "C", "D", "D", "B"], ["B", "D", "D", "A", "A", "B"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 66')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
67 | {
"construction_cdl": [
"Shape(QT,TR,RQ)",
"Shape(TS,SR,RT)",
"Collinear(QTS)"
],
"text_cdl": [
"Equal(LengthOfLine(QT),x)",
"Equal(LengthOfLine(RQ),6)",
"Equal(LengthOfLine(SQ),18)",
"Equal(LengthOfLine(SR),14)",
"Equal(MeasureOfAngle(TRQ),MeasureOfAngle(SRT))"
],
"image_cdl": [
"Equal(LengthOfLine(QT),x)",
"Equal(LengthOfLine(RQ),6)",
"Equal(LengthOfLine(SQ),18)",
"Equal(LengthOfLine(SR),14)",
"Equal(MeasureOfAngle(TRQ),MeasureOfAngle(SRT))"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, QT=x, RQ=6, SQ=18, SR=14, ∠TRQ=∠SRT. Find the value of x. | 如图所示，QT=x，RQ=6，SQ=18，SR=14，∠TRQ=∠SRT。求x的值。 | 27/5 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [6.123233995736766e-17, 1.0], "S": [-1.0, 1.2246467991473532e-16], "T": [-1.8369701987210297e-16, -1.0], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.5000000000000001, -0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.5000000000000004, -0.8660254037844384], "G": [0.5000000000000001, -0.8660254037844386], "H": [-0.5000000000000004, -0.8660254037844384], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["Q", "T", "T", "R", "R", "Q"], ["T", "S", "S", "R", "R", "T"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 67')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
68 | {
"construction_cdl": [
"Shape(AC,CD,DA)",
"Shape(DC,CB,BD)",
"Collinear(ADB)"
],
"text_cdl": [
"Equal(LengthOfLine(AD),5)",
"Equal(LengthOfLine(BC),32)",
"Equal(LengthOfLine(CD),12)",
"PerpendicularBetweenLine(AC,BC)",
"PerpendicularBetweenLine(BD,CD)",
"SimilarBetweenTriangle(ACB,CDB)"
],
"image_cdl": [
"PerpendicularBetweenLine(AC,BC)",
"PerpendicularBetweenLine(BD,CD)"
],
"goal_cdl": "Value(PerimeterOfTriangle(ACB))"
} | As shown in the diagram, AD=5, BC=32, CD=12, AC⊥BC, BD⊥CD, triangle ACB is similar to triangle CDB.. Find the perimeter of triangle ACB. | 如图所示，AD=5，BC=32，CD=12，AC垂直于BC，BD垂直于CD，三角形ACB相似于三角形CDB。求△ACB的周长。 | sqrt(1193)+45 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [6.123233995736766e-17, 1.0], "S": [-1.0, 1.2246467991473532e-16], "T": [-1.8369701987210297e-16, -1.0], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.5000000000000001, -0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-1.0, 1.2246467991473532e-16], "D": [-1.8369701987210297e-16, -1.0], "L": [-0.8660254037844387, 0.49999999999999994], "E": [-1.0, 1.2246467991473532e-16], "F": [-0.5000000000000004, -0.8660254037844384], "G": [0.5000000000000001, -0.8660254037844386], "H": [-0.5000000000000004, -0.8660254037844384], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["A", "C", "C", "D", "D", "A"], ["D", "C", "C", "B", "B", "D"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 68')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
69 | {
"construction_cdl": [
"Shape(DE,EG,GD)",
"Shape(DG,GF,FD)",
"Collinear(EGF)"
],
"text_cdl": [
"Equal(MeasureOfAngle(DEF),25)",
"Equal(MeasureOfAngle(GFD),65)",
"PerpendicularBetweenLine(EG,DG)"
],
"image_cdl": [
"Equal(MeasureOfAngle(DEF),25)",
"Equal(MeasureOfAngle(GFD),65)",
"PerpendicularBetweenLine(EG,DG)"
],
"goal_cdl": "Value(MeasureOfAngle(FDG))"
} | As shown in the diagram, ∠DEF=25°, ∠GFD=65°, EG⊥DG. Find the measure of ∠FDG. | 如图所示，∠DEF=25°，∠GFD=65°，EG垂直于DG。求∠FDG的大小。 | 25 | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [6.123233995736766e-17, 1.0], "S": [-1.0, 1.2246467991473532e-16], "T": [-1.8369701987210297e-16, -1.0], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-1.0, 1.2246467991473532e-16], "N": [-0.8660254037844388, -0.4999999999999997], "P": [0.30901699437494723, -0.9510565162951536], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.5000000000000001, -0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-1.0, 1.2246467991473532e-16], "D": [1.0, 0.0], "L": [-0.8660254037844387, 0.49999999999999994], "E": [6.123233995736766e-17, 1.0], "F": [-1.0, 1.2246467991473532e-16], "G": [-1.8369701987210297e-16, -1.0], "H": [-0.5000000000000004, -0.8660254037844384], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["D", "E", "E", "G", "G", "D"], ["D", "G", "G", "F", "F", "D"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 69')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() | |
70 | {
"construction_cdl": [
"Shape(AKJ,JK)",
"Shape(KJ,AJN,NM,AMK)",
"Shape(AMK,ML,LK)",
"Shape(ANM,MN)",
"Collinear(LKJ)",
"Collinear(LMN)",
"Cocircular(A,KJNM)"
],
"text_cdl": [
"Equal(LengthOfLine(JK),12)",
"Equal(LengthOfLine(LK),2)",
"Equal(LengthOfLine(ML),x)",
"Equal(LengthOfLine(MN),6)"
],
"image_cdl": [
"Equal(LengthOfLine(JK),12)",
"Equal(LengthOfLine(LK),2)",
"Equal(LengthOfLine(ML),x)",
"Equal(LengthOfLine(MN),6)"
],
"goal_cdl": "Value(x)"
} | As shown in the diagram, JK=12, LK=2, ML=x, MN=6. Find the value of x. | 如图所示，JK=12，LK=2，ML=x，MN=6。求x的值。 | -3+sqrt(37) | import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np
def draw_geometry():
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_aspect('equal')
points = {"R": [6.123233995736766e-17, 1.0], "S": [-1.0, 1.2246467991473532e-16], "T": [-1.8369701987210297e-16, -1.0], "X": [-1.8369701987210297e-16, -1.0], "Y": [0.5000000000000001, -0.8660254037844386], "Z": [0.8660254037844384, -0.5000000000000004], "M": [-0.5000000000000004, -0.8660254037844384], "N": [0.5000000000000001, -0.8660254037844386], "P": [0.30901699437494723, -0.9510565162951536], "Q": [1.0, 0.0], "A": [1.0, 0.0], "B": [6.123233995736766e-17, 1.0], "J": [0.5000000000000001, 0.8660254037844386], "K": [-0.4999999999999998, 0.8660254037844387], "W": [-0.5000000000000004, -0.8660254037844384], "C": [-1.0, 1.2246467991473532e-16], "D": [1.0, 0.0], "L": [-1.0, 1.2246467991473532e-16], "E": [6.123233995736766e-17, 1.0], "F": [-1.0, 1.2246467991473532e-16], "G": [-1.8369701987210297e-16, -1.0], "H": [-0.5000000000000004, -0.8660254037844384], "I": [6.123233995736766e-17, 1.0], "O": [0.30901699437494723, -0.9510565162951536], "U": [-0.5000000000000004, -0.8660254037844384], "V": [0.5000000000000001, 0.8660254037844386]}
shapes = [["A", "K", "J", "J", "K"], ["K", "J", "A", "J", "N", "N", "M", "A", "M", "K"], ["A", "M", "K", "M", "L", "L", "K"], ["A", "N", "M", "M", "N"]]
for pts in shapes:
coords = [points[p] for p in pts if p in points]
if len(coords) > 1:
poly = patches.Polygon(coords, closed=True, fill=False, edgecolor='blue', linewidth=2)
ax.add_patch(poly)
for pt, (x, y) in points.items():
ax.plot(x, y, 'ro')
ax.text(x, y, f' {pt}', fontsize=12)
ax.set_title('Problem 70')
ax.autoscale_view()
plt.show()
if __name__ == '__main__':
draw_geometry() |
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