id int32 1 6.98k | annotation stringclasses 132
values | source stringlengths 7 17 | problem_level int32 0 28 | problem_text_cn stringlengths 20 201 | problem_text_en stringlengths 58 424 | problem_img stringlengths 5 8 | construction_cdl listlengths 1 28 | text_cdl listlengths 0 16 | image_cdl listlengths 0 16 | goal_cdl stringlengths 8 131 | problem_answer stringclasses 906
values | theorem_seqs listlengths 0 28 | theorem_seqs_dag_json stringlengths 13 3.3k | image imagewidth (px) 48 1.6k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | XiaokaiZhang_2023-03-12 | Geometry3k-0 | 1 | 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。 | 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. | 1.png | [
"Shape(RS,ST,TR)",
"Shape(XY,YZ,ZX)"
] | [
"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)"
] | [
"Equal(LengthOfLine(TR),x+21)",
"Equal(LengthOfLine(ZX),2*x-14)",
"Equal(MeasureOfAngle(TRS),4*y-10)",
"Equal(MeasureOfAngle(ZXY),3*y+5)"
] | Value(y) | 15 | [
"congruent_triangle_property_angle_equal(1,RST,XYZ)"
] | {"START": ["congruent_triangle_property_angle_equal(1,RST,XYZ)"]} | |
2 | XiaokaiZhang_2023-04-02 | Geometry3k-1 | 1 | 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。 | 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. | 2.png | [
"Shape(MR,RQ,QM)",
"Shape(QR,RP,PQ)",
"Shape(MQ,QN,NM)",
"Shape(QP,PN,NQ)",
"Collinear(MQP)",
"Collinear(RQN)"
] | [
"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(Measur... | [
"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(Measur... | Value(y) | 13/2 | [
"parallelogram_property_opposite_line_equal(1,MRPN)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,MRPN)"]} | |
3 | XiaokaiZhang_2023-04-02 | Geometry3k-2 | 3 | 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。 | 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. | 3.png | [
"Shape(RA,AB,BS,SR)",
"Shape(AJ,JK,KB,BA)",
"Shape(JQ,QT,TK,KJ)",
"Collinear(RAJQ)",
"Collinear(SBKT)"
] | [
"Equal(LengthOfLine(BT),LengthOfLine(SB))",
"Equal(LengthOfLine(QA),LengthOfLine(RA))",
"Equal(LengthOfLine(QT),86)",
"Equal(LengthOfLine(RS),54)",
"IsMidsegmentOfQuadrilateral(JK,AQTB)"
] | [
"Equal(LengthOfLine(BT),LengthOfLine(SB))",
"Equal(LengthOfLine(QA),LengthOfLine(RA))",
"Equal(LengthOfLine(QT),86)",
"Equal(LengthOfLine(RS),54)"
] | Value(LengthOfLine(JK)) | 78 | [
"midsegment_of_quadrilateral_judgment_midpoint(1,AB,RQTS)",
"midsegment_of_quadrilateral_property_length(1,AB,RQTS)",
"midsegment_of_quadrilateral_property_length(1,JK,AQTB)"
] | {"START": ["midsegment_of_quadrilateral_judgment_midpoint(1,AB,RQTS)", "midsegment_of_quadrilateral_property_length(1,JK,AQTB)"], "midsegment_of_quadrilateral_judgment_midpoint(1,AB,RQTS)": ["midsegment_of_quadrilateral_property_length(1,AB,RQTS)"]} | |
4 | XiaokaiZhang_2023-04-02 | Geometry3k-3 | 1 | 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。 | 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. | 4.png | [
"Shape(WX,XY,YZ,ZW)"
] | [
"Equal(LengthOfLine(WZ),23)",
"Equal(LengthOfLine(XY),23)",
"Equal(MeasureOfAngle(ZWX),112)",
"ParallelBetweenLine(XW,YZ)",
"Trapezoid(XYZW)"
] | [
"Equal(LengthOfLine(WZ),23)",
"Equal(LengthOfLine(XY),23)",
"Equal(MeasureOfAngle(ZWX),112)",
"ParallelBetweenLine(XW,YZ)"
] | Value(MeasureOfAngle(YZW)) | 68 | [
"parallel_property_ipsilateral_internal_angle(1,ZY,WX)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,ZY,WX)"]} | |
5 | XiaokaiZhang_2023-03-12 | Geometry3k-4 | 3 | 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。 | As shown in the diagram, AB=y, AD=z, BC=x, BD=4, CD=10, AB⊥CB, DC⊥AC. Find the value of x. | 5.png | [
"Shape(CA,AB,BC)",
"Shape(CB,BD,DC)",
"Collinear(ABD)"
] | [
"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)"
] | [
"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)"
] | Value(x) | 2*sqrt(21) | [
"adjacent_complementary_angle(1,ABC,CBD)",
"right_triangle_judgment_angle(1,CBD)",
"right_triangle_property_pythagorean(1,CBD)"
] | {"START": ["adjacent_complementary_angle(1,ABC,CBD)"], "adjacent_complementary_angle(1,ABC,CBD)": ["right_triangle_judgment_angle(1,CBD)"], "right_triangle_judgment_angle(1,CBD)": ["right_triangle_property_pythagorean(1,CBD)"]} | |
6 | XiaokaiZhang_2023-03-12 | Geometry3k-5 | 6 | 如图所示，AC=20，CM=12，MB=30，CM⊥AM。求三角形AMB的周长。 | As shown in the diagram, AC=20, CM=12, MB=30, CM is perpendicular to AM. Find the perimeter of △AMB. | 6.png | [
"Shape(AC,CM,MA)",
"Shape(AM,MB,BA)",
"Collinear(CMB)"
] | [
"Equal(LengthOfLine(AC),20)",
"Equal(LengthOfLine(CM),12)",
"Equal(LengthOfLine(MB),30)",
"PerpendicularBetweenLine(CM,AM)"
] | [
"Equal(LengthOfLine(AC),20)",
"Equal(LengthOfLine(CM),12)",
"Equal(LengthOfLine(MB),30)",
"PerpendicularBetweenLine(CM,AM)"
] | Value(PerimeterOfTriangle(AMB)) | 80 | [
"adjacent_complementary_angle(1,CMA,AMB)",
"right_triangle_judgment_angle(1,CMA)",
"right_triangle_judgment_angle(1,AMB)",
"right_triangle_property_pythagorean(1,CMA)",
"right_triangle_property_pythagorean(1,AMB)",
"triangle_perimeter_formula(1,AMB)"
] | {"START": ["adjacent_complementary_angle(1,CMA,AMB)", "right_triangle_judgment_angle(1,CMA)", "triangle_perimeter_formula(1,AMB)"], "adjacent_complementary_angle(1,CMA,AMB)": ["right_triangle_judgment_angle(1,AMB)"], "right_triangle_judgment_angle(1,AMB)": ["right_triangle_property_pythagorean(1,AMB)"], "right_triangle_judgment_angle(1,CMA)": ["right_triangle_property_pythagorean(1,CMA)"]} | |
7 | XiaokaiZhang_2023-03-12 | Geometry3k-6 | 3 | 如图所示，TR=7*sqrt(2)，TS=3*sqrt(2)，RS垂直于TS。求∠STR的大小。 | As shown in the diagram, TR=7*sqrt(2), TS=3*sqrt(2), RS is perpendicular to TS. Find the measure of ∠STR. | 7.png | [
"Shape(TR,RS,ST)"
] | [
"Equal(LengthOfLine(TR),7*sqrt(2))",
"Equal(LengthOfLine(TS),3*sqrt(2))",
"PerpendicularBetweenLine(RS,TS)"
] | [
"Equal(LengthOfLine(TR),7*sqrt(2))",
"Equal(LengthOfLine(TS),3*sqrt(2))",
"PerpendicularBetweenLine(RS,TS)"
] | Value(MeasureOfAngle(STR)) | 180*asin(2*sqrt(10)/7)/pi | [
"right_triangle_judgment_angle(1,RST)",
"right_triangle_property_pythagorean(1,RST)",
"sine_theorem(1,RST)"
] | {"START": ["right_triangle_judgment_angle(1,RST)", "sine_theorem(1,RST)"], "right_triangle_judgment_angle(1,RST)": ["right_triangle_property_pythagorean(1,RST)"]} | |
8 | XiaokaiZhang_2023-03-12 | Geometry3k-7 | 2 | 如图所示，AB=4/7，AC=x，BC=5/7，BA垂直于CA。求x的值。 | As shown in the diagram, AB=4/7, AC=x, BC=5/7, BA⊥CA. Find the value of x. | 8.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),4/7)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),5/7)",
"PerpendicularBetweenLine(BA,CA)"
] | [
"Equal(LengthOfLine(AB),4/7)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),5/7)",
"PerpendicularBetweenLine(BA,CA)"
] | Value(x) | 3/7 | [
"right_triangle_judgment_angle(1,BAC)",
"right_triangle_property_pythagorean(1,BAC)"
] | {"START": ["right_triangle_judgment_angle(1,BAC)"], "right_triangle_judgment_angle(1,BAC)": ["right_triangle_property_pythagorean(1,BAC)"]} | |
9 | XiaokaiZhang_2023-04-02 | Geometry3k-8 | 11 | 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。 | 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. | 9.png | [
"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)"
] | [
"Equal(LengthOfLine(JK),10)",
"Equal(LengthOfLine(MN),16)",
"Equal(MeasureOfArc(KMN),98)",
"IsCentreOfCircle(K,K)",
"PerpendicularBetweenLine(MP,KP)"
] | [
"Equal(LengthOfLine(JK),10)",
"IsCentreOfCircle(K,K)",
"PerpendicularBetweenLine(MP,KP)"
] | Value(LengthOfLine(LN)) | 4*sqrt(5) | [
"circle_property_chord_perpendicular_bisect_chord(1,K,KP,MN)",
"line_addition(1,MP,PN)",
"radius_of_circle_property_length_equal(1,KJ,K)",
"radius_of_circle_property_length_equal(1,KM,K)",
"radius_of_circle_property_length_equal(1,KL,K)",
"right_triangle_judgment_angle(1,MPK)",
"right_triangle_property_... | {"START": ["circle_property_chord_perpendicular_bisect_chord(1,K,KP,MN)", "line_addition(1,MP,PN)", "radius_of_circle_property_length_equal(1,KJ,K)", "radius_of_circle_property_length_equal(1,KM,K)", "radius_of_circle_property_length_equal(1,KL,K)", "right_triangle_judgment_angle(1,MPK)", "line_addition(1,LP,PK)", "vertical_angle(1,MPK,NPL)"], "right_triangle_judgment_angle(1,MPK)": ["right_triangle_property_pythagorean(1,MPK)"], "right_triangle_judgment_angle(1,NPL)": ["right_triangle_property_pythagorean(1,NPL)"], "vertical_angle(1,MPK,NPL)": ["right_triangle_judgment_angle(1,NPL)"]} | |
10 | XiaokaiZhang_2023-04-02 | Geometry3k-9 | 1 | 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。 | 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. | 10.png | [
"Shape(EDB,BF,EFD)",
"Shape(CD,EFD,FC)",
"Shape(FB,EBF)",
"Collinear(BFC)",
"Cocircular(E,FDB)"
] | [
"Equal(MeasureOfAngle(FCD),x)",
"Equal(MeasureOfArc(EDB),10*x)",
"Equal(MeasureOfArc(EFD),40)",
"IsTangentOfCircle(CD,E)"
] | [
"Equal(MeasureOfAngle(FCD),x)",
"Equal(MeasureOfArc(EDB),10*x)",
"Equal(MeasureOfArc(EFD),40)"
] | Value(x) | 5 | [
"circle_property_circular_power_tangent_and_segment_angle(2,CD,CFB,E)"
] | {"START": ["circle_property_circular_power_tangent_and_segment_angle(2,CD,CFB,E)"]} | |
11 | XiaokaiZhang_2023-03-12 | Geometry3k-10 | 1 | 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。 | 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. | 11.png | [
"Shape(KA,AH,HK)",
"Shape(KH,HC,CK)",
"Shape(KC,CF,FK)",
"Shape(KF,FG,GK)",
"Shape(GF,FE,EG)",
"Collinear(AHCF)",
"Collinear(EGK)"
] | [
"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)"
] | [
"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)"
] | Value(MeasureOfAngle(FEK)) | 55 | [
"triangle_property_angle_sum(1,FEK)"
] | {"START": ["triangle_property_angle_sum(1,FEK)"]} | |
12 | XiaokaiZhang_2023-04-02 | Geometry3k-11 | 8 | 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。 | 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. | 12.png | [
"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)"
] | [
"Equal(LengthOfLine(AB),30)",
"Equal(LengthOfLine(CD),30)",
"Equal(MeasureOfArc(XCZ),40)",
"IsCentreOfCircle(X,X)",
"PerpendicularBetweenLine(AM,YM)",
"PerpendicularBetweenLine(DN,ZN)"
] | [
"Equal(LengthOfLine(AB),30)",
"Equal(LengthOfLine(CD),30)",
"Equal(MeasureOfArc(XCZ),40)",
"IsCentreOfCircle(X,X)",
"PerpendicularBetweenLine(AM,YM)",
"PerpendicularBetweenLine(DN,ZN)"
] | Value(MeasureOfArc(XBA)) | 80 | [
"vertical_angle(1,CNX,DNZ)",
"circle_property_chord_perpendicular_bisect_arc(1,XCD,XNZ)",
"arc_addition_length(1,XCZ,XZD)",
"similar_arc_judgment_cocircular(1,XCZ,XCD)",
"similar_arc_property_length_ratio(1,XCZ,XCD)",
"similar_arc_property_measure_ratio(1,XCZ,XCD)",
"congruent_arc_judgment_chord_equal(1... | {"START": ["vertical_angle(1,CNX,DNZ)", "arc_addition_length(1,XCZ,XZD)", "similar_arc_judgment_cocircular(1,XCZ,XCD)", "congruent_arc_judgment_chord_equal(1,XCD,XBA)"], "congruent_arc_judgment_chord_equal(1,XCD,XBA)": ["congruent_arc_property_measure_equal(1,XCD,XBA)"], "similar_arc_judgment_cocircular(1,XCZ,XCD)": ["similar_arc_property_length_ratio(1,XCZ,XCD)", "similar_arc_property_measure_ratio(1,XCZ,XCD)"], "vertical_angle(1,CNX,DNZ)": ["circle_property_chord_perpendicular_bisect_arc(1,XCD,XNZ)"]} | |
13 | XiaokaiZhang_2023-04-02 | Geometry3k-12 | 3 | 如图所示，AB=5，BD=x，CA=15/2，EC=9/2。求x的值。 | As shown in the diagram, AB=5, BD=x, CA=15/2, EC=9/2. Find the value of x. | 13.png | [
"Shape(XDB,BD)",
"Shape(BA,AC,XBC)",
"Shape(DB,XBC,CE,XED)",
"Shape(XCE,EC)",
"Collinear(ABXD)",
"Collinear(ACE)",
"Cocircular(X,BCED)"
] | [
"Equal(LengthOfLine(AB),5)",
"Equal(LengthOfLine(BD),x)",
"Equal(LengthOfLine(CA),15/2)",
"Equal(LengthOfLine(EC),9/2)"
] | [
"Equal(LengthOfLine(AB),5)",
"Equal(LengthOfLine(BD),x)",
"Equal(LengthOfLine(CA),15/2)",
"Equal(LengthOfLine(EC),9/2)"
] | Value(x) | 13 | [
"circle_property_circular_power_segment_and_segment_line(1,ABD,ACE,X)",
"line_addition(1,AB,BD)",
"line_addition(1,AC,CE)"
] | {"START": ["circle_property_circular_power_segment_and_segment_line(1,ABD,ACE,X)", "line_addition(1,AB,BD)", "line_addition(1,AC,CE)"]} | |
14 | XiaokaiZhang_2023-04-02 | Geometry3k-13 | 1 | 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。 | 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. | 14.png | [
"Shape(AC,CJ,JA)",
"Shape(JC,CB,BJ)",
"Shape(AJ,JD,DA)",
"Shape(JB,BD,DJ)",
"Collinear(AJB)",
"Collinear(CJD)"
] | [
"Equal(LengthOfLine(AJ),2*x+3)",
"Equal(LengthOfLine(CJ),8*y-36)",
"Equal(LengthOfLine(JB),5*x)",
"Equal(LengthOfLine(JD),4*y)",
"Parallelogram(ACBD)"
] | [
"Equal(LengthOfLine(AJ),2*x+3)",
"Equal(LengthOfLine(CJ),8*y-36)",
"Equal(LengthOfLine(JB),5*x)",
"Equal(LengthOfLine(JD),4*y)"
] | Value(y) | 9 | [
"parallelogram_property_diagonal_bisection(1,CBDA,J)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,CBDA,J)"]} | |
15 | XiaokaiZhang_2023-04-02 | Geometry3k-14 | 4 | 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。 | 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. | 15.png | [
"Shape(JI,IL,LN,NJ)",
"Shape(IB,BD,DL,LI)",
"Shape(CJ,JN)",
"Collinear(CJIB)",
"Collinear(NLD)"
] | [
"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)"
] | [
"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)"
] | Value(x) | 48 | [
"parallel_judgment_corresponding_angle(1,JN,BD,C)",
"trapezoid_judgment_parallel(1,JBDN)",
"parallel_judgment_corresponding_angle(1,IL,BD,J)",
"midsegment_of_quadrilateral_judgment_parallel(3,IL,JBDN)"
] | {"START": ["parallel_judgment_corresponding_angle(1,JN,BD,C)", "parallel_judgment_corresponding_angle(1,IL,BD,J)"], "parallel_judgment_corresponding_angle(1,IL,BD,J)": ["midsegment_of_quadrilateral_judgment_parallel(3,IL,JBDN)"], "parallel_judgment_corresponding_angle(1,JN,BD,C)": ["trapezoid_judgment_parallel(1,JBDN)"], "trapezoid_judgment_parallel(1,JBDN)": ["midsegment_of_quadrilateral_judgment_parallel(3,IL,JBDN)"]} | |
16 | XiaokaiZhang_2023-03-12 | Geometry3k-15 | 1 | 如图所示，AB=10，AC=y，BC=x，∠ABC=60°，BC垂直于AC。求y的值。 | As shown in the diagram, AB=10, AC=y, BC=x, ∠ABC=60°, BC is perpendicular to AC. Find the value of y. | 16.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),y)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(ABC),60)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),y)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(ABC),60)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(y) | 5*sqrt(3) | [
"sine_theorem(1,ABC)"
] | {"START": ["sine_theorem(1,ABC)"]} | |
17 | XiaokaiZhang_2023-04-02 | Geometry3k-16 | 5 | 如图所示，AB=8，AD=27，AE=12，CD平行于BE。求直线BC的长度。 | As shown in the diagram, AB=8, AD=27, AE=12, CD is parallel to BE. Find the length of line BC. | 17.png | [
"Shape(CB,BE,ED,DC)",
"Shape(BA,AE,EB)",
"Collinear(ABC)",
"Collinear(AED)"
] | [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(AD),27)",
"Equal(LengthOfLine(AE),12)",
"ParallelBetweenLine(CD,BE)"
] | [
"ParallelBetweenLine(CD,BE)"
] | Value(LengthOfLine(BC)) | 10 | [
"parallel_property_corresponding_angle(1,EB,DC,A)",
"similar_triangle_judgment_aa(1,BAE,CAD)",
"similar_triangle_property_line_ratio(1,BAE,CAD)",
"similar_triangle_property_line_ratio(1,EBA,DCA)",
"line_addition(1,AB,BC)"
] | {"START": ["parallel_property_corresponding_angle(1,EB,DC,A)", "line_addition(1,AB,BC)"], "parallel_property_corresponding_angle(1,EB,DC,A)": ["similar_triangle_judgment_aa(1,BAE,CAD)"], "similar_triangle_judgment_aa(1,BAE,CAD)": ["similar_triangle_property_line_ratio(1,BAE,CAD)", "similar_triangle_property_line_ratio(1,EBA,DCA)"]} | |
18 | XiaokaiZhang_2023-04-02 | Geometry3k-17 | 1 | 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。 | As shown in the diagram, ∠NMQ=10*x°, ∠PNM=20*x°, ∠PNM=∠MQP, ∠QPN=∠NMQ, MQPN is a parallelogram. Find the measure of ∠MQP. | 18.png | [
"Shape(MQ,QP,PN,NM)"
] | [
"Equal(MeasureOfAngle(NMQ),10*x)",
"Equal(MeasureOfAngle(PNM),20*x)",
"Equal(MeasureOfAngle(PNM),MeasureOfAngle(MQP))",
"Equal(MeasureOfAngle(QPN),MeasureOfAngle(NMQ))",
"Parallelogram(MQPN)"
] | [
"Equal(MeasureOfAngle(PNM),MeasureOfAngle(MQP))",
"Equal(MeasureOfAngle(QPN),MeasureOfAngle(NMQ))"
] | Value(MeasureOfAngle(MQP)) | 120 | [
"parallel_property_ipsilateral_internal_angle(1,NP,MQ)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,NP,MQ)"]} | |
19 | XiaokaiZhang_2023-04-02 | Geometry3k-18 | 1 | 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。 | 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. | 19.png | [
"Shape(AC,CB,BA)",
"Shape(BC,CD,DB)"
] | [
"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)"
] | [
"Equal(LengthOfLine(AB),4*x-17)",
"Equal(LengthOfLine(CD),2*x-1)",
"Equal(MeasureOfAngle(BCD),4*y-19)",
"Equal(MeasureOfAngle(CBA),3*y+3)"
] | Value(y) | 22 | [
"parallel_property_alternate_interior_angle(2,AB,CD)"
] | {"START": ["parallel_property_alternate_interior_angle(2,AB,CD)"]} | |
20 | XiaokaiZhang_2023-03-12 | Geometry3k-19 | 4 | 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)。 | As shown in the diagram, AE=BE, BA=8, BC=8, BE=CE, DA=10, DC=10, ∠ADE=x°, DE⊥AE. Find sin(x). | 20.png | [
"Shape(AD,DE,EA)",
"Shape(AE,EB,BA)",
"Shape(ED,DC,CE)",
"Shape(BE,EC,CB)",
"Collinear(DEB)",
"Collinear(AEC)"
] | [
"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)"
] | [
"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)"
] | Value(Sin(x)) | 2*sqrt(2)/5 | [
"adjacent_complementary_angle(1,DEA,AEB)",
"right_triangle_judgment_angle(1,AEB)",
"right_triangle_property_pythagorean(1,AEB)",
"sine_theorem(1,ADE)"
] | {"START": ["adjacent_complementary_angle(1,DEA,AEB)", "sine_theorem(1,ADE)"], "adjacent_complementary_angle(1,DEA,AEB)": ["right_triangle_judgment_angle(1,AEB)"], "right_triangle_judgment_angle(1,AEB)": ["right_triangle_property_pythagorean(1,AEB)"]} | |
21 | XiaokaiZhang_2023-04-02 | Geometry3k-20 | 1 | 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。 | 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. | 21.png | [
"Shape(AB,BX,XC,CA)"
] | [
"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)"
] | [
"Equal(MeasureOfAngle(ABX),5*y-6)",
"Equal(MeasureOfAngle(BXC),2*x+24)",
"Equal(MeasureOfAngle(CAB),3*x-17)",
"Equal(MeasureOfAngle(XCA),y+58)"
] | Value(y) | 16 | [
"parallelogram_property_opposite_angle_equal(1,BXCA)"
] | {"START": ["parallelogram_property_opposite_angle_equal(1,BXCA)"]} | |
22 | XiaokaiZhang_2023-04-02 | Geometry3k-21 | 3 | 如图所示，∠NJK=101°，JA∥NF。求∠HNJ的大小。 | As shown in the diagram, ∠NJK=101°, JA is parallel to NF. Find the measure of ∠HNJ. | 22.png | [
"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)"
] | [
"Equal(MeasureOfAngle(NJK),101)",
"ParallelBetweenLine(JA,NF)"
] | [
"ParallelBetweenLine(JA,NF)"
] | Value(MeasureOfAngle(HNJ)) | 79 | [
"parallel_property_collinear_extend(1,JA,NF,K)",
"parallel_property_collinear_extend(2,FN,JK,H)",
"parallel_property_ipsilateral_internal_angle(1,NH,JK)"
] | {"START": ["parallel_property_collinear_extend(1,JA,NF,K)"], "parallel_property_collinear_extend(1,JA,NF,K)": ["parallel_property_collinear_extend(2,FN,JK,H)"], "parallel_property_collinear_extend(2,FN,JK,H)": ["parallel_property_ipsilateral_internal_angle(1,NH,JK)"]} | |
23 | XiaokaiZhang_2023-03-12 | Geometry3k-23 | 0 | 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。 | 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. | 23.png | [
"Shape(RS,ST,TR)"
] | [
"Equal(LengthOfLine(SR),3*x-5)",
"Equal(LengthOfLine(TR),2*x+7)",
"Equal(LengthOfLine(TS),22)",
"IsoscelesTriangle(RST)"
] | [
"Equal(LengthOfLine(SR),3*x-5)",
"Equal(LengthOfLine(TR),2*x+7)",
"Equal(LengthOfLine(TS),22)"
] | Value(LengthOfLine(RS)) | 31 | [] | {"START": []} | |
24 | XiaokaiZhang_2023-04-02 | Geometry3k-24 | 1 | 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。 | As shown in the diagram, YX=24, YZ=28, ∠XWZ=105°, quadrilateral WZYX is a ▱. Find the measure of ∠WZY. | 24.png | [
"Shape(WZ,ZY,YX,XW)"
] | [
"Equal(LengthOfLine(YX),24)",
"Equal(LengthOfLine(YZ),28)",
"Equal(MeasureOfAngle(XWZ),105)",
"Parallelogram(WZYX)"
] | [
"Equal(LengthOfLine(YX),24)",
"Equal(LengthOfLine(YZ),28)",
"Equal(MeasureOfAngle(XWZ),105)"
] | Value(MeasureOfAngle(WZY)) | 75 | [
"parallel_property_ipsilateral_internal_angle(1,WX,ZY)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,WX,ZY)"]} | |
25 | XiaokaiZhang_2023-03-12 | Geometry3k-25 | 3 | 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。 | 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. | 25.png | [
"Shape(CA,AD,DC)",
"Shape(DA,AB,BD)",
"Collinear(BDC)"
] | [
"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)"
] | [
"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)"
] | Value(x) | 6*sqrt(3) | [
"adjacent_complementary_angle(1,BDA,ADC)",
"triangle_property_angle_sum(1,BDA)",
"sine_theorem(1,BDA)"
] | {"START": ["adjacent_complementary_angle(1,BDA,ADC)", "triangle_property_angle_sum(1,BDA)", "sine_theorem(1,BDA)"]} | |
26 | XiaokaiZhang_2023-03-12 | Geometry3k-26 | 2 | 如图所示，AB=y，AC=x，BC=18，∠ABC=30°，CA⊥BA。求y的值。 | As shown in the diagram, AB=y, AC=x, BC=18, ∠ABC=30°, CA is perpendicular to BA. Find the value of y. | 26.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),18)",
"Equal(MeasureOfAngle(ABC),30)",
"PerpendicularBetweenLine(CA,BA)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),18)",
"Equal(MeasureOfAngle(ABC),30)",
"PerpendicularBetweenLine(CA,BA)"
] | Value(y) | 9*sqrt(3) | [
"triangle_property_angle_sum(1,ABC)",
"sine_theorem(1,BCA)"
] | {"START": ["triangle_property_angle_sum(1,ABC)", "sine_theorem(1,BCA)"]} | |
27 | XiaokaiZhang_2023-04-02 | Geometry3k-27 | 4 | 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。 | 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. | 27.png | [
"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)"
] | [
"Equal(DiameterOfCircle(H),18)",
"Equal(LengthOfLine(LM),12)",
"Equal(MeasureOfArc(HML),84)",
"IsCentreOfCircle(H,H)",
"PerpendicularBetweenLine(MP,HP)"
] | [
"IsCentreOfCircle(H,H)",
"PerpendicularBetweenLine(MP,HP)"
] | Value(MeasureOfArc(HKL)) | 42 | [
"circle_property_chord_perpendicular_bisect_arc(1,HML,HPK)",
"congruent_arc_judgment_length_equal(1,HMK,HKL)",
"congruent_arc_property_measure_equal(1,HMK,HKL)",
"arc_addition_measure(1,HMK,HKL)"
] | {"START": ["circle_property_chord_perpendicular_bisect_arc(1,HML,HPK)", "arc_addition_measure(1,HMK,HKL)"], "circle_property_chord_perpendicular_bisect_arc(1,HML,HPK)": ["congruent_arc_judgment_length_equal(1,HMK,HKL)"], "congruent_arc_judgment_length_equal(1,HMK,HKL)": ["congruent_arc_property_measure_equal(1,HMK,HKL)"]} | |
28 | XiaokaiZhang_2023-04-02 | Geometry3k-28 | 2 | 如图所示，∠CHE=9*x-11°，∠GDF=8*x+4°，BD∥EH。求x的值。 | As shown in the diagram, ∠CHE=9*x-11°, ∠GDF=8*x+4°, BD is parallel to EH. Find the value of x. | 28.png | [
"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)"
] | [
"Equal(MeasureOfAngle(CHE),9*x-11)",
"Equal(MeasureOfAngle(GDF),8*x+4)",
"ParallelBetweenLine(BD,EH)"
] | [
"Equal(MeasureOfAngle(CHE),9*x-11)",
"Equal(MeasureOfAngle(GDF),8*x+4)"
] | Value(x) | 15 | [
"vertical_angle(1,GDF,HDB)",
"parallel_property_corresponding_angle(1,HE,DB,C)"
] | {"START": ["vertical_angle(1,GDF,HDB)", "parallel_property_corresponding_angle(1,HE,DB,C)"]} | |
29 | XiaokaiZhang_2023-03-12 | Geometry3k-29 | 1 | 如图所示，RS=5，TR=6，TS=3，∠SRT=x°。求x的值。 | As shown in the diagram, RS=5, TR=6, TS=3, ∠SRT=x°. Find the value of x. | 29.png | [
"Shape(SR,RT,TS)"
] | [
"Equal(LengthOfLine(RS),5)",
"Equal(LengthOfLine(TR),6)",
"Equal(LengthOfLine(TS),3)",
"Equal(MeasureOfAngle(SRT),x)"
] | [
"Equal(LengthOfLine(RS),5)",
"Equal(LengthOfLine(TR),6)",
"Equal(LengthOfLine(TS),3)",
"Equal(MeasureOfAngle(SRT),x)"
] | Value(x) | 180*acos(13/15)/pi | [
"cosine_theorem(1,RTS)"
] | {"START": ["cosine_theorem(1,RTS)"]} | |
30 | XiaokaiZhang_2023-04-02 | Geometry3k-30 | 2 | 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。 | 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. | 30.png | [
"Shape(CD,DE,EF,FC)",
"Shape(BL,LA,AN,NB)"
] | [
"Equal(AreaOfQuadrilateral(BLAN),72)",
"Equal(AreaOfQuadrilateral(CDEF),50)",
"Equal(LengthOfLine(BN),6)",
"Equal(LengthOfLine(CF),x)",
"SimilarBetweenQuadrilateral(CDEF,BLAN)"
] | [
"Equal(AreaOfQuadrilateral(BLAN),72)",
"Equal(AreaOfQuadrilateral(CDEF),50)",
"Equal(LengthOfLine(BN),6)",
"Equal(LengthOfLine(CF),x)"
] | Value(x) | 5 | [
"similar_quadrilateral_property_area_square_ratio(1,CDEF,BLAN)",
"similar_quadrilateral_property_line_ratio(1,FCDE,NBLA)"
] | {"START": ["similar_quadrilateral_property_area_square_ratio(1,CDEF,BLAN)", "similar_quadrilateral_property_line_ratio(1,FCDE,NBLA)"]} | |
31 | XiaokaiZhang_2023-04-02 | Geometry3k-31 | 2 | 如图所示，∠ACD=x°，∠ECA=2*x°，∠GCE=x°。求x的值。 | As shown in the diagram, ∠ACD=x°, ∠ECA=2*x°, ∠GCE=x°. Find the value of x. | 31.png | [
"Shape(GC,CE)",
"Shape(EC,CA)",
"Shape(GC,CA)",
"Shape(EC,CD)",
"Shape(AC,CD)",
"Collinear(GCD)"
] | [
"Equal(MeasureOfAngle(ACD),x)",
"Equal(MeasureOfAngle(ECA),2*x)",
"Equal(MeasureOfAngle(GCE),x)"
] | [
"Equal(MeasureOfAngle(ACD),x)",
"Equal(MeasureOfAngle(ECA),2*x)",
"Equal(MeasureOfAngle(GCE),x)"
] | Value(x) | 45 | [
"angle_addition(1,GCE,ECA)",
"adjacent_complementary_angle(1,GCA,ACD)"
] | {"START": ["angle_addition(1,GCE,ECA)", "adjacent_complementary_angle(1,GCA,ACD)"]} | |
32 | XiaokaiZhang_2023-04-02 | Geometry3k-32 | 1 | 如图所示，∠DFH=4*x°，∠HFA=2*x-6°。求∠DFH的大小。 | As shown in the diagram, ∠DFH=4*x°, ∠HFA=2*x-6°. Find the measure of ∠DFH. | 32.png | [
"Shape(DF,FH)",
"Shape(HF,FA)",
"Shape(AF,FB)",
"Shape(BF,FD)",
"Collinear(DFA)",
"Collinear(BFH)"
] | [
"Equal(MeasureOfAngle(DFH),4*x)",
"Equal(MeasureOfAngle(HFA),2*x-6)"
] | [] | Value(MeasureOfAngle(DFH)) | 124 | [
"adjacent_complementary_angle(1,DFH,HFA)"
] | {"START": ["adjacent_complementary_angle(1,DFH,HFA)"]} | |
33 | XiaokaiZhang_2023-04-02 | Geometry3k-33 | 0 | 如图所示，AB=2*x+3，BC=5*x，ADCB是菱形。求x的值。 | As shown in the diagram, AB=2*x+3, BC=5*x, ADCB is a rhombus. Find the value of x. | 33.png | [
"Shape(AD,DE,EA)",
"Shape(ED,DC,CE)",
"Shape(EC,CB,BE)",
"Shape(BA,AE,EB)",
"Collinear(AEC)",
"Collinear(DEB)"
] | [
"Equal(LengthOfLine(AB),2*x+3)",
"Equal(LengthOfLine(BC),5*x)",
"Rhombus(ADCB)"
] | [] | Value(x) | 1 | [] | {"START": []} | |
34 | XiaokaiZhang_2023-04-02 | Geometry3k-34 | 3 | 如图所示，OA=3，∠AOB=45°，O是圆O的圆心。求弧OBA的长度。 | As shown in the diagram, OA=3, ∠AOB=45°, the center of ⊙O is O. Find the length of ⌒OBA. | 34.png | [
"Shape(OA,OAB,BO)",
"Shape(AO,OB,OBA)",
"Cocircular(O,AB)"
] | [
"Equal(LengthOfLine(OA),3)",
"Equal(MeasureOfAngle(AOB),45)",
"IsCentreOfCircle(O,O)"
] | [
"Equal(LengthOfLine(OA),3)",
"Equal(MeasureOfAngle(AOB),45)",
"IsCentreOfCircle(O,O)"
] | Value(LengthOfArc(OBA)) | 3*pi/4 | [
"arc_property_center_angle(1,OBA,O)",
"radius_of_circle_property_length_equal(1,OA,O)",
"arc_length_formula(1,OBA)"
] | {"START": ["arc_property_center_angle(1,OBA,O)", "radius_of_circle_property_length_equal(1,OA,O)", "arc_length_formula(1,OBA)"]} | |
35 | XiaokaiZhang_2023-04-02 | Geometry3k-35 | 2 | 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。 | 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. | 35.png | [
"Shape(QV,VS,SR,RQ)",
"Shape(VU,UT,TS,SV)",
"Collinear(QVU)",
"Collinear(RST)"
] | [
"Equal(LengthOfLine(QR),2)",
"Equal(LengthOfLine(VS),7)",
"IsMidpointOfLine(S,RT)",
"IsMidpointOfLine(V,QU)",
"Trapezoid(QUTR)"
] | [] | Value(LengthOfLine(UT)) | 12 | [
"midsegment_of_quadrilateral_judgment_midpoint(1,VS,QUTR)",
"midsegment_of_quadrilateral_property_length(1,VS,QUTR)"
] | {"START": ["midsegment_of_quadrilateral_judgment_midpoint(1,VS,QUTR)"], "midsegment_of_quadrilateral_judgment_midpoint(1,VS,QUTR)": ["midsegment_of_quadrilateral_property_length(1,VS,QUTR)"]} | |
36 | XiaokaiZhang_2023-04-02 | Geometry3k-36 | 2 | 如图所示，∠ABD=130°，∠CBA=x°，∠DBC=95°。求x的值。 | As shown in the diagram, ∠ABD=130°, ∠CBA=x°, ∠DBC=95°. Find the value of x. | 36.png | [
"Shape(BAC,CB,BA)",
"Shape(BDA,AB,BD)",
"Shape(BCD,DB,BC)"
] | [
"Equal(MeasureOfAngle(ABD),130)",
"Equal(MeasureOfAngle(CBA),x)",
"Equal(MeasureOfAngle(DBC),95)"
] | [
"Equal(MeasureOfAngle(ABD),130)",
"Equal(MeasureOfAngle(CBA),x)",
"Equal(MeasureOfAngle(DBC),95)"
] | Value(x) | 135 | [
"angle_addition(1,ABD,DBC)",
"round_angle(1,CBA,ABC)"
] | {"START": ["angle_addition(1,ABD,DBC)", "round_angle(1,CBA,ABC)"]} | |
37 | XiaokaiZhang_2023-04-02 | Geometry3k-37 | 2 | 如图所示，∠DMN=56°，∠GLI=3*y-11°，∠HNK=4*x°，LI平行于MD，MD∥NS。求x的值。 | 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. | 37.png | [
"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)"
] | [
"Equal(MeasureOfAngle(DMN),56)",
"Equal(MeasureOfAngle(GLI),3*y-11)",
"Equal(MeasureOfAngle(HNK),4*x)",
"ParallelBetweenLine(LI,MD)",
"ParallelBetweenLine(MD,NS)"
] | [
"Equal(MeasureOfAngle(DMN),56)",
"Equal(MeasureOfAngle(GLI),3*y-11)",
"Equal(MeasureOfAngle(HNK),4*x)",
"ParallelBetweenLine(LI,MD)",
"ParallelBetweenLine(MD,NS)"
] | Value(x) | 31 | [
"vertical_angle(1,HNK,MNS)",
"parallel_property_ipsilateral_internal_angle(1,MD,NS)"
] | {"START": ["vertical_angle(1,HNK,MNS)", "parallel_property_ipsilateral_internal_angle(1,MD,NS)"]} | |
38 | XiaokaiZhang_2023-03-12 | Geometry3k-38 | 3 | 如图所示，AB=y，AC=8，BC=x，∠BAC=60°，AC垂直于BC。求x的值。 | As shown in the diagram, AB=y, AC=8, BC=x, ∠BAC=60°, AC is perpendicular to BC. Find the value of x. | 38.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),8)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(BAC),60)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),8)",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(BAC),60)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(x) | 8*sqrt(3) | [
"triangle_property_angle_sum(1,ACB)",
"sine_theorem(1,ACB)",
"sine_theorem(1,BAC)"
] | {"START": ["triangle_property_angle_sum(1,ACB)", "sine_theorem(1,ACB)", "sine_theorem(1,BAC)"]} | |
39 | XiaokaiZhang_2023-04-02 | Geometry3k-39 | 3 | 如图所示，EJ=6，LK=7，ML=4，JMLK是平行四边形，JE⊥LE。求JMLK的周长。 | 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. | 39.png | [
"Shape(JM,ME,EJ)",
"Shape(JE,EL,LK,KJ)",
"Collinear(MEL)"
] | [
"Equal(LengthOfLine(EJ),6)",
"Equal(LengthOfLine(LK),7)",
"Equal(LengthOfLine(ML),4)",
"Parallelogram(JMLK)",
"PerpendicularBetweenLine(JE,LE)"
] | [
"Equal(LengthOfLine(EJ),6)",
"Equal(LengthOfLine(LK),7)",
"Equal(LengthOfLine(ML),4)",
"PerpendicularBetweenLine(JE,LE)"
] | Value(PerimeterOfQuadrilateral(JMLK)) | 22 | [
"parallelogram_property_opposite_line_equal(1,JMLK)",
"parallelogram_property_opposite_line_equal(1,MLKJ)",
"quadrilateral_perimeter_formula(1,JMLK)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,JMLK)", "parallelogram_property_opposite_line_equal(1,MLKJ)", "quadrilateral_perimeter_formula(1,JMLK)"]} | |
40 | XiaokaiZhang_2023-03-12 | Geometry3k-40 | 6 | 如图所示，AB=8，AC=14，BC=8，BX=x，BX⊥CX。求x的值。 | As shown in the diagram, AB=8, AC=14, BC=8, BX=x, BX⊥CX. Find the value of x. | 40.png | [
"Shape(BA,AX,XB)",
"Shape(BX,XC,CB)",
"Collinear(AXC)"
] | [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(AC),14)",
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BX),x)",
"PerpendicularBetweenLine(BX,CX)"
] | [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(AC),14)",
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BX),x)",
"PerpendicularBetweenLine(BX,CX)"
] | Value(x) | sqrt(15) | [
"adjacent_complementary_angle(1,AXB,BXC)",
"line_addition(1,AX,XC)",
"right_triangle_judgment_angle(1,AXB)",
"right_triangle_judgment_angle(1,BXC)",
"right_triangle_property_pythagorean(1,AXB)",
"right_triangle_property_pythagorean(1,BXC)"
] | {"START": ["adjacent_complementary_angle(1,AXB,BXC)", "line_addition(1,AX,XC)", "right_triangle_judgment_angle(1,BXC)"], "adjacent_complementary_angle(1,AXB,BXC)": ["right_triangle_judgment_angle(1,AXB)"], "right_triangle_judgment_angle(1,AXB)": ["right_triangle_property_pythagorean(1,AXB)"], "right_triangle_judgment_angle(1,BXC)": ["right_triangle_property_pythagorean(1,BXC)"]} | |
41 | XiaokaiZhang_2023-03-12 | Geometry3k-41 | 3 | 如图所示，NM=4，∠NLM=∠PLN，∠PLN=25°，LM⊥NM，NP⊥LP。求∠MNP的大小。 | As shown in the diagram, NM=4, ∠NLM=∠PLN, ∠PLN=25°, LM⊥NM, NP⊥LP. Find the measure of ∠MNP. | 41.png | [
"Shape(LM,MN,NL)",
"Shape(LN,NP,PL)"
] | [
"Equal(LengthOfLine(NM),4)",
"Equal(MeasureOfAngle(NLM),MeasureOfAngle(PLN))",
"Equal(MeasureOfAngle(PLN),25)",
"PerpendicularBetweenLine(LM,NM)",
"PerpendicularBetweenLine(NP,LP)"
] | [
"Equal(LengthOfLine(NM),4)",
"Equal(MeasureOfAngle(NLM),MeasureOfAngle(PLN))",
"Equal(MeasureOfAngle(PLN),25)",
"PerpendicularBetweenLine(LM,NM)",
"PerpendicularBetweenLine(NP,LP)"
] | Value(MeasureOfAngle(MNP)) | 130 | [
"triangle_property_angle_sum(1,LMN)",
"triangle_property_angle_sum(1,LNP)",
"angle_addition(1,MNL,LNP)"
] | {"START": ["triangle_property_angle_sum(1,LMN)", "triangle_property_angle_sum(1,LNP)", "angle_addition(1,MNL,LNP)"]} | |
42 | XiaokaiZhang_2023-03-12 | Geometry3k-42 | 6 | 如图所示，GF=12，HG=6，HJ=8，JK=x-4，GJ∥FK。求x的值。 | As shown in the diagram, GF=12, HG=6, HJ=8, JK=x-4, GJ is parallel to FK. Find the value of x. | 42.png | [
"Shape(HG,GJ,JH)",
"Shape(GF,FK,KJ,JG)",
"Collinear(HGF)",
"Collinear(KJH)"
] | [
"Equal(LengthOfLine(GF),12)",
"Equal(LengthOfLine(HG),6)",
"Equal(LengthOfLine(HJ),8)",
"Equal(LengthOfLine(JK),x-4)",
"ParallelBetweenLine(GJ,FK)"
] | [] | Value(x) | 20 | [
"parallel_property_corresponding_angle(1,GJ,FK,H)",
"similar_triangle_judgment_aa(1,JHG,KHF)",
"line_addition(1,HG,GF)",
"line_addition(1,HJ,JK)",
"similar_triangle_property_line_ratio(1,JHG,KHF)",
"similar_triangle_property_line_ratio(1,GJH,FKH)"
] | {"START": ["parallel_property_corresponding_angle(1,GJ,FK,H)", "line_addition(1,HG,GF)", "line_addition(1,HJ,JK)"], "parallel_property_corresponding_angle(1,GJ,FK,H)": ["similar_triangle_judgment_aa(1,JHG,KHF)"], "similar_triangle_judgment_aa(1,JHG,KHF)": ["similar_triangle_property_line_ratio(1,JHG,KHF)", "similar_triangle_property_line_ratio(1,GJH,FKH)"]} | |
43 | XiaokaiZhang_2023-04-02 | Geometry3k-43 | 1 | 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。 | 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. | 43.png | [
"Shape(NM,ML,LN)",
"Shape(LM,MR,RL)",
"Shape(NL,LQ,QN)",
"Shape(LR,RQ,QL)",
"Collinear(NLR)",
"Collinear(MLQ)"
] | [
"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)"
] | [
"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)"
] | Value(w) | 12 | [
"parallelogram_property_diagonal_bisection(1,MRQN,L)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,MRQN,L)"]} | |
44 | XiaokaiZhang_2023-03-12 | Geometry3k-44 | 2 | 如图所示，BA=6，CA=x，CB=x，∠BAC=45°，∠CBA=45°，AC⊥BC。求x的值。 | 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. | 44.png | [
"Shape(CB,BA,AC)"
] | [
"Equal(LengthOfLine(BA),6)",
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CB),x)",
"Equal(MeasureOfAngle(BAC),45)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(BA),6)",
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CB),x)",
"Equal(MeasureOfAngle(BAC),45)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(x) | 3*sqrt(2) | [
"right_triangle_judgment_angle(1,ACB)",
"right_triangle_property_pythagorean(1,ACB)"
] | {"START": ["right_triangle_judgment_angle(1,ACB)"], "right_triangle_judgment_angle(1,ACB)": ["right_triangle_property_pythagorean(1,ACB)"]} | |
45 | XiaokaiZhang_2023-04-02 | Geometry3k-45 | 1 | 如图所示，∠YVW=25°，⌒AXZ的角度为110，弧AYW的角度为x。求x的值。 | 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. | 45.png | [
"Shape(YV,VW,AYW)",
"Shape(AZY,YZ)",
"Shape(AYW,WX,AXZ,ZY)",
"Shape(AWX,XW)",
"Collinear(VYZ)",
"Collinear(VWX)",
"Cocircular(A,ZYWX)"
] | [
"Equal(MeasureOfAngle(YVW),25)",
"Equal(MeasureOfArc(AXZ),110)",
"Equal(MeasureOfArc(AYW),x)"
] | [
"Equal(MeasureOfAngle(YVW),25)",
"Equal(MeasureOfArc(AXZ),110)",
"Equal(MeasureOfArc(AYW),x)"
] | Value(x) | 60 | [
"circle_property_circular_power_segment_and_segment_angle(1,VYZ,VWX,A)"
] | {"START": ["circle_property_circular_power_segment_and_segment_angle(1,VYZ,VWX,A)"]} | |
46 | XiaokaiZhang_2023-04-02 | Geometry3k-46 | 4 | 如图所示，KJ=11，∠JKL=65°，圆K的圆心为K。求扇形KJL的面积。 | As shown in the diagram, KJ=11, ∠JKL=65°, the center of circle K is K. Find the area of the sector KJL. | 46.png | [
"Shape(KJ,KJL,LK)",
"Shape(JK,KL,KLJ)",
"Cocircular(K,JL)"
] | [
"Equal(LengthOfLine(KJ),11)",
"Equal(MeasureOfAngle(JKL),65)",
"IsCentreOfCircle(K,K)"
] | [
"Equal(LengthOfLine(KJ),11)",
"Equal(MeasureOfAngle(JKL),65)",
"IsCentreOfCircle(K,K)"
] | Value(AreaOfSector(KJL)) | 7139*pi/72 | [
"round_angle(1,JKL,LKJ)",
"radius_of_circle_property_length_equal(1,KJ,K)",
"arc_property_center_angle(1,KJL,K)",
"sector_area_formula(1,KJL)"
] | {"START": ["round_angle(1,JKL,LKJ)", "radius_of_circle_property_length_equal(1,KJ,K)", "arc_property_center_angle(1,KJL,K)", "sector_area_formula(1,KJL)"]} | |
47 | XiaokaiZhang_2023-04-02 | Geometry3k-47 | 15 | 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。 | 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. | 47.png | [
"Shape(SP,PA,AS)",
"Shape(SA,AZ,ZR,RS)",
"Shape(RZ,ZQ,QR)",
"Collinear(PAZQ)"
] | [
"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)",
"PerpendicularBetwee... | [
"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)",
"PerpendicularBetwee... | Value(PerimeterOfQuadrilateral(SPQR)) | 6*sqrt(2)+6*sqrt(3)+38 | [
"triangle_property_angle_sum(1,RZQ)",
"sine_theorem(1,RZQ)",
"sine_theorem(1,QRZ)",
"altitude_of_quadrilateral_judgment_left_vertex(2,SA,SPQR)",
"adjacent_complementary_angle(1,PZR,RZQ)",
"altitude_of_quadrilateral_judgment_right_vertex(2,RZ,SPQR)",
"parallel_judgment_corresponding_angle(1,AS,ZR,P)",
... | {"START": ["triangle_property_angle_sum(1,RZQ)", "sine_theorem(1,RZQ)", "sine_theorem(1,QRZ)", "altitude_of_quadrilateral_judgment_left_vertex(2,SA,SPQR)", "adjacent_complementary_angle(1,PZR,RZQ)", "triangle_property_angle_sum(1,SPA)", "sine_theorem(1,SPA)", "line_addition(1,PA,AZ)", "line_addition(1,PZ,ZQ)", "quadrilateral_perimeter_formula(1,SPQR)"], "adjacent_complementary_angle(1,PZR,RZQ)": ["altitude_of_quadrilateral_judgment_right_vertex(2,RZ,SPQR)", "parallel_judgment_corresponding_angle(1,AS,ZR,P)"], "parallel_judgment_corresponding_angle(1,AS,ZR,P)": ["parallelogram_judgment_parallel_and_parallel(1,SAZR)"], "parallelogram_judgment_parallel_and_parallel(1,SAZR)": ["parallelogram_property_opposite_line_equal(1,AZRS)"], "triangle_property_angle_sum(1,SPA)": ["isosceles_triangle_judgment_angle_equal(1,ASP)"]} | |
48 | XiaokaiZhang_2023-04-02 | Geometry3k-48 | 4 | 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。 | 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. | 48.png | [
"Shape(EY,YQ,QF,FE)",
"Shape(YM,MA,AQ,QY)",
"Collinear(EYM)",
"Collinear(FQA)"
] | [
"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)"
] | [
"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)"
] | Value(y) | 40 | [
"parallel_property_corresponding_angle(2,AM,QY,F)",
"parallelogram_judgment_parallel_and_parallel(1,YMAQ)",
"parallelogram_property_opposite_angle_equal(1,YMAQ)",
"adjacent_complementary_angle(1,EYQ,QYM)"
] | {"START": ["parallel_property_corresponding_angle(2,AM,QY,F)", "parallelogram_judgment_parallel_and_parallel(1,YMAQ)", "adjacent_complementary_angle(1,EYQ,QYM)"], "parallelogram_judgment_parallel_and_parallel(1,YMAQ)": ["parallelogram_property_opposite_angle_equal(1,YMAQ)"]} | |
49 | XiaokaiZhang_2023-04-02 | Geometry3k-49 | 2 | 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。 | As shown in the diagram, ∠AXW=82°, ∠YXA=33°, quadrilateral XWZY is a ▱. Find the measure of ∠WZY. | 49.png | [
"Shape(XW,WA,AX)",
"Shape(AW,WZ,ZA)",
"Shape(AZ,ZY,YA)",
"Shape(XA,AY,YX)",
"Collinear(XAZ)",
"Collinear(WAY)"
] | [
"Equal(MeasureOfAngle(AXW),82)",
"Equal(MeasureOfAngle(YXA),33)",
"Parallelogram(XWZY)"
] | [
"Equal(MeasureOfAngle(AXW),82)",
"Equal(MeasureOfAngle(YXA),33)"
] | Value(MeasureOfAngle(WZY)) | 115 | [
"angle_addition(1,YXA,AXW)",
"parallelogram_property_opposite_angle_equal(1,XWZY)"
] | {"START": ["angle_addition(1,YXA,AXW)", "parallelogram_property_opposite_angle_equal(1,XWZY)"]} | |
50 | XiaokaiZhang_2023-03-12 | Geometry3k-50 | 4 | 如图所示，FE=6，FG=3，FH=4，HG=2，△DEF相似于△GFH。求△DEF的周长。 | 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. | 50.png | [
"Shape(DE,EF,FD)",
"Shape(CD,DF,FG,GC)",
"Shape(GF,FH,HG)",
"Collinear(CDE)",
"Collinear(EFH)",
"Collinear(HGC)"
] | [
"Equal(LengthOfLine(FE),6)",
"Equal(LengthOfLine(FG),3)",
"Equal(LengthOfLine(FH),4)",
"Equal(LengthOfLine(HG),2)",
"SimilarBetweenTriangle(DEF,GFH)"
] | [
"Equal(LengthOfLine(FE),6)",
"Equal(LengthOfLine(FG),3)",
"Equal(LengthOfLine(FH),4)",
"Equal(LengthOfLine(HG),2)"
] | Value(PerimeterOfTriangle(DEF)) | 27/2 | [
"similar_triangle_property_line_ratio(1,DEF,GFH)",
"similar_triangle_property_line_ratio(1,FDE,HGF)",
"similar_triangle_property_line_ratio(1,EFD,FHG)",
"triangle_perimeter_formula(1,DEF)"
] | {"START": ["similar_triangle_property_line_ratio(1,DEF,GFH)", "similar_triangle_property_line_ratio(1,FDE,HGF)", "similar_triangle_property_line_ratio(1,EFD,FHG)", "triangle_perimeter_formula(1,DEF)"]} | |
51 | XiaokaiZhang_2023-04-02 | Geometry3k-51 | 1 | 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。 | 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. | 51.png | [
"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(EX... | [
"Equal(MeasureOfAngle(LWX),3*a+40)",
"Equal(MeasureOfAngle(WXE),2*a+25)",
"Equal(MeasureOfAngle(XZK),5*b-26)",
"ParallelBetweenLine(WL,XE)",
"ParallelBetweenLine(XN,ZK)"
] | [
"ParallelBetweenLine(WL,XE)",
"ParallelBetweenLine(XN,ZK)"
] | Value(a) | 23 | [
"parallel_property_ipsilateral_internal_angle(1,WL,XE)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,WL,XE)"]} | |
52 | XiaokaiZhang_2023-03-12 | Geometry3k-52 | 1 | 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。 | 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. | 52.png | [
"Shape(DG,GF,FD)",
"Shape(FG,GA,AF)",
"Shape(BG,GC,CB)",
"Shape(AB,BC,CA)",
"Collinear(DFA)",
"Collinear(ABG)"
] | [
"Equal(MeasureOfAngle(AGC),40)",
"Equal(MeasureOfAngle(DGF),53)",
"PerpendicularBetweenLine(CB,GB)",
"PerpendicularBetweenLine(FG,CG)",
"PerpendicularBetweenLine(GF,DF)"
] | [
"PerpendicularBetweenLine(CB,GB)",
"PerpendicularBetweenLine(FG,CG)",
"PerpendicularBetweenLine(GF,DF)"
] | Value(MeasureOfAngle(FDG)) | 37 | [
"triangle_property_angle_sum(1,DGF)"
] | {"START": ["triangle_property_angle_sum(1,DGF)"]} | |
53 | XiaokaiZhang_2023-04-02 | Geometry3k-53 | 4 | 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。 | As shown in the diagram, ∠FOE=45°, the center of circle O is O, CO⊥AO, EO⊥BO. Find the measure of arc OAE. | 53.png | [
"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)"
] | [
"Equal(MeasureOfAngle(FOE),45)",
"IsCentreOfCircle(O,O)",
"PerpendicularBetweenLine(CO,AO)",
"PerpendicularBetweenLine(EO,BO)"
] | [
"Equal(MeasureOfAngle(FOE),45)",
"IsCentreOfCircle(O,O)",
"PerpendicularBetweenLine(CO,AO)",
"PerpendicularBetweenLine(EO,BO)"
] | Value(MeasureOfArc(OAE)) | 270 | [
"adjacent_complementary_angle(1,EOB,BOC)",
"angle_addition(1,EOB,BOC)",
"angle_addition(1,EOC,COA)",
"arc_property_center_angle(1,OAE,O)"
] | {"START": ["adjacent_complementary_angle(1,EOB,BOC)", "angle_addition(1,EOB,BOC)", "angle_addition(1,EOC,COA)", "arc_property_center_angle(1,OAE,O)"]} | |
54 | XiaokaiZhang_2023-04-02 | Geometry3k-54 | 8 | 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。 | 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. | 54.png | [
"Shape(DC,CB,BH,ODH)",
"Shape(OD,ODH,HO)",
"Collinear(DOH)",
"Cocircular(O,DH)"
] | [
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BH),12)",
"IsCentreOfCircle(O,O)",
"Rectangle(DCBH)"
] | [
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(BH),12)",
"IsCentreOfCircle(O,O)"
] | Value(Sub(AreaOfQuadrilateral(DCBH),AreaOfSector(ODH))) | 96-8*pi | [
"parallelogram_area_formula_sine(1,CBHD)",
"diameter_of_circle_judgment_pass_centre(1,DOH,O)",
"parallelogram_property_opposite_line_equal(1,CBHD)",
"diameter_of_circle_property_length_equal(1,DH,O)",
"circle_property_length_of_radius_and_diameter(1,O)",
"flat_angle(1,HOD)",
"arc_property_center_angle(1... | {"START": ["parallelogram_area_formula_sine(1,CBHD)", "diameter_of_circle_judgment_pass_centre(1,DOH,O)", "parallelogram_property_opposite_line_equal(1,CBHD)", "circle_property_length_of_radius_and_diameter(1,O)", "flat_angle(1,HOD)", "arc_property_center_angle(1,ODH,O)", "sector_area_formula(1,ODH)"], "diameter_of_circle_judgment_pass_centre(1,DOH,O)": ["diameter_of_circle_property_length_equal(1,DH,O)"]} | |
55 | XiaokaiZhang_2023-03-12 | Geometry3k-55 | 2 | 如图所示，AB=10，AC=6，BC=x，AC垂直于BC。求x的值。 | As shown in the diagram, AB=10, AC=6, BC=x, AC⊥BC. Find the value of x. | 55.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),6)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),6)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(x) | 8 | [
"right_triangle_judgment_angle(1,ACB)",
"right_triangle_property_pythagorean(1,ACB)"
] | {"START": ["right_triangle_judgment_angle(1,ACB)"], "right_triangle_judgment_angle(1,ACB)": ["right_triangle_property_pythagorean(1,ACB)"]} | |
56 | XiaokaiZhang_2023-03-12 | Geometry3k-56 | 0 | 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。 | 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. | 56.png | [
"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)"
] | [
"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)"
] | [
"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)"
] | Value(MeasureOfAngle(CAD)) | 33 | [] | {"START": []} | |
57 | XiaokaiZhang_2023-04-02 | Geometry3k-57 | 0 | 如图所示，AB=14，DP⊥AP，四边形ADCB是菱形。求直线BC的长度。 | As shown in the diagram, AB=14, DP is perpendicular to AP, ADCB is a rhombus. Find the length of line BC. | 57.png | [
"Shape(AD,DP,PA)",
"Shape(PD,DC,CP)",
"Shape(PC,CB,BP)",
"Shape(AP,PB,BA)",
"Collinear(APC)",
"Collinear(DPB)"
] | [
"Equal(LengthOfLine(AB),14)",
"PerpendicularBetweenLine(DP,AP)",
"Rhombus(ADCB)"
] | [
"PerpendicularBetweenLine(DP,AP)"
] | Value(LengthOfLine(BC)) | 14 | [] | {"START": []} | |
58 | XiaokaiZhang_2023-04-02 | Geometry3k-58 | 3 | 如图所示，∠BCE=∠EBC，∠DAG=136°，∠DEA=47°，∠EFB=63°，∠FED=69°。求∠EBC的大小。 | As shown in the diagram, ∠BCE=∠EBC, ∠DAG=136°, ∠DEA=47°, ∠EFB=63°, ∠FED=69°. Find the measure of ∠EBC. | 58.png | [
"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)"
] | [
"Equal(MeasureOfAngle(BCE),MeasureOfAngle(EBC))",
"Equal(MeasureOfAngle(DAG),136)",
"Equal(MeasureOfAngle(DEA),47)",
"Equal(MeasureOfAngle(EFB),63)",
"Equal(MeasureOfAngle(FED),69)"
] | [
"Equal(MeasureOfAngle(DAG),136)",
"Equal(MeasureOfAngle(DEA),47)",
"Equal(MeasureOfAngle(EFB),63)",
"Equal(MeasureOfAngle(FED),69)"
] | Value(MeasureOfAngle(EBC)) | 32 | [
"angle_addition(1,FED,DEA)",
"vertical_angle(1,FEA,CEB)",
"triangle_property_angle_sum(1,EBC)"
] | {"START": ["angle_addition(1,FED,DEA)", "vertical_angle(1,FEA,CEB)", "triangle_property_angle_sum(1,EBC)"]} | |
59 | XiaokaiZhang_2023-04-02 | Geometry3k-59 | 2 | 如图所示，∠LWX=53°，WL∥XE，XN平行于ZK。求∠XZK的大小。 | As shown in the diagram, ∠LWX=53°, WL∥XE, XN is parallel to ZK. Find the measure of ∠XZK. | 59.png | [
"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(EX... | [
"Equal(MeasureOfAngle(LWX),53)",
"ParallelBetweenLine(WL,XE)",
"ParallelBetweenLine(XN,ZK)"
] | [
"ParallelBetweenLine(WL,XE)",
"ParallelBetweenLine(XN,ZK)"
] | Value(MeasureOfAngle(XZK)) | 53 | [
"parallel_property_corresponding_angle(2,WL,XE,N)",
"parallel_property_corresponding_angle(1,XN,ZK,E)"
] | {"START": ["parallel_property_corresponding_angle(2,WL,XE,N)", "parallel_property_corresponding_angle(1,XN,ZK,E)"]} | |
60 | XiaokaiZhang_2023-03-12 | Geometry3k-60 | 8 | 如图所示，AC=x，AD=4，BC=y，BD=9，CD=z，AC⊥BC，BD⊥CD。求z的值。 | As shown in the diagram, AC=x, AD=4, BC=y, BD=9, CD=z, AC⊥BC, BD⊥CD. Find the value of z. | 60.png | [
"Shape(AC,CD,DA)",
"Shape(DC,CB,BD)",
"Collinear(BDA)"
] | [
"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)"
] | [
"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)"
] | Value(z) | 6 | [
"line_addition(1,AD,DB)",
"adjacent_complementary_angle(1,BDC,CDA)",
"right_triangle_judgment_angle(1,ACB)",
"right_triangle_judgment_angle(1,BDC)",
"right_triangle_judgment_angle(1,CDA)",
"right_triangle_property_pythagorean(1,ACB)",
"right_triangle_property_pythagorean(1,BDC)",
"right_triangle_prope... | {"START": ["line_addition(1,AD,DB)", "adjacent_complementary_angle(1,BDC,CDA)", "right_triangle_judgment_angle(1,ACB)", "right_triangle_judgment_angle(1,BDC)"], "adjacent_complementary_angle(1,BDC,CDA)": ["right_triangle_judgment_angle(1,CDA)"], "right_triangle_judgment_angle(1,ACB)": ["right_triangle_property_pythagorean(1,ACB)"], "right_triangle_judgment_angle(1,BDC)": ["right_triangle_property_pythagorean(1,BDC)"], "right_triangle_judgment_angle(1,CDA)": ["right_triangle_property_pythagorean(1,CDA)"]} | |
61 | XiaokaiZhang_2023-03-12 | Geometry3k-61 | 1 | 如图所示，AB=8，CA=10，CB=a，∠BAC=60°。求a的值。 | As shown in the diagram, AB=8, CA=10, CB=a, ∠BAC=60°. Find the value of a. | 61.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(CA),10)",
"Equal(LengthOfLine(CB),a)",
"Equal(MeasureOfAngle(BAC),60)"
] | [
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(CA),10)",
"Equal(LengthOfLine(CB),a)",
"Equal(MeasureOfAngle(BAC),60)"
] | Value(a) | 2*sqrt(21) | [
"cosine_theorem(1,ACB)"
] | {"START": ["cosine_theorem(1,ACB)"]} | |
62 | XiaokaiZhang_2023-04-02 | Geometry3k-62 | 7 | 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。 | 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. | 62.png | [
"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)"
] | [
"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)"
] | [
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(CE,FE)",
"PerpendicularBetweenLine(FD,AD)"
] | Value(x) | 8 | [
"adjacent_complementary_angle(1,BDF,FDA)",
"circle_property_chord_perpendicular_bisect_chord(1,F,FD,BA)",
"circle_property_chord_perpendicular_bisect_chord(1,F,FE,CB)",
"line_addition(1,BD,DA)",
"line_addition(1,BE,EC)",
"mirror_congruent_triangle_judgment_hl(2,BDF,BFE)",
"mirror_congruent_triangle_prop... | {"START": ["adjacent_complementary_angle(1,BDF,FDA)", "circle_property_chord_perpendicular_bisect_chord(1,F,FE,CB)", "line_addition(1,BD,DA)", "line_addition(1,BE,EC)"], "adjacent_complementary_angle(1,BDF,FDA)": ["circle_property_chord_perpendicular_bisect_chord(1,F,FD,BA)", "mirror_congruent_triangle_judgment_hl(2,BDF,BFE)"], "circle_property_chord_perpendicular_bisect_chord(1,F,FD,BA)": ["mirror_congruent_triangle_judgment_hl(2,BDF,BFE)"], "circle_property_chord_perpendicular_bisect_chord(1,F,FE,CB)": ["mirror_congruent_triangle_judgment_hl(2,BDF,BFE)", "mirror_congruent_triangle_judgment_hl(2,BDF,BFE)"], "line_addition(1,BD,DA)": ["mirror_congruent_triangle_judgment_hl(2,BDF,BFE)"], "line_addition(1,BE,EC)": ["mirror_congruent_triangle_judgment_hl(2,BDF,BFE)"], "mirror_congruent_triangle_judgment_hl(2,BDF,BFE)": ["mirror_congruent_triangle_property_line_equal(1,BDF,BFE)"]} | |
63 | XiaokaiZhang_2023-04-02 | Geometry3k-63 | 1 | 如图所示，∠CFD=x+36°，∠DEC=2*y°，∠ECF=78°，∠FDE=110°，CE平行于FD。求y的值。 | 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. | 63.png | [
"Shape(EC,CF,FD,DE)"
] | [
"Equal(MeasureOfAngle(CFD),x+36)",
"Equal(MeasureOfAngle(DEC),2*y)",
"Equal(MeasureOfAngle(ECF),78)",
"Equal(MeasureOfAngle(FDE),110)",
"ParallelBetweenLine(CE,FD)"
] | [
"Equal(MeasureOfAngle(CFD),x+36)",
"Equal(MeasureOfAngle(DEC),2*y)",
"Equal(MeasureOfAngle(ECF),78)",
"Equal(MeasureOfAngle(FDE),110)",
"ParallelBetweenLine(CE,FD)"
] | Value(y) | 35 | [
"parallel_property_ipsilateral_internal_angle(1,DF,EC)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,DF,EC)"]} | |
64 | XiaokaiZhang_2023-04-02 | Geometry3k-64 | 2 | 如图所示，∠AJH=x°，∠HGB=2*x°，GB垂直于HB，JH⊥GH。求∠BHG的大小。 | As shown in the diagram, ∠AJH=x°, ∠HGB=2*x°, GB⊥HB, JH is perpendicular to GH. Find the measure of ∠BHG. | 64.png | [
"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)"
] | [
"Equal(MeasureOfAngle(AJH),x)",
"Equal(MeasureOfAngle(HGB),2*x)",
"PerpendicularBetweenLine(GB,HB)",
"PerpendicularBetweenLine(JH,GH)"
] | [
"PerpendicularBetweenLine(GB,HB)",
"PerpendicularBetweenLine(JH,GH)"
] | Value(MeasureOfAngle(BHG)) | 30 | [
"triangle_property_angle_sum(1,GJH)",
"triangle_property_angle_sum(1,GBH)"
] | {"START": ["triangle_property_angle_sum(1,GJH)", "triangle_property_angle_sum(1,GBH)"]} | |
65 | XiaokaiZhang_2023-04-02 | Geometry3k-65 | 2 | 如图所示，∠CBD=55°，∠FBG=35°，圆B的圆心为B。求⌒BCD的角度。 | As shown in the diagram, ∠CBD=55°, ∠FBG=35°, B is the center of circle B. Find the measure of arc BCD. | 65.png | [
"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)"
] | [
"Equal(MeasureOfAngle(CBD),55)",
"Equal(MeasureOfAngle(FBG),35)",
"IsCentreOfCircle(B,B)"
] | [
"Equal(MeasureOfAngle(CBD),55)",
"Equal(MeasureOfAngle(FBG),35)",
"IsCentreOfCircle(B,B)"
] | Value(MeasureOfArc(BCD)) | 305 | [
"round_angle(1,CBD,DBC)",
"arc_property_center_angle(1,BCD,B)"
] | {"START": ["round_angle(1,CBD,DBC)", "arc_property_center_angle(1,BCD,B)"]} | |
66 | XiaokaiZhang_2023-03-12 | Geometry3k-66 | 2 | 如图所示，BA=3*x-13，BC=2*x+5，∠BCD=∠CDB，∠BDA=∠DAB，∠DBC=60°。求x的值。 | As shown in the diagram, BA=3*x-13, BC=2*x+5, ∠BCD=∠CDB, ∠BDA=∠DAB, ∠DBC=60°. Find the value of x. | 66.png | [
"Shape(BC,CD,DB)",
"Shape(BD,DA,AB)"
] | [
"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)"
] | [
"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)"
] | Value(x) | 18 | [
"isosceles_triangle_judgment_angle_equal(1,BCD)",
"isosceles_triangle_judgment_angle_equal(1,BDA)"
] | {"START": ["isosceles_triangle_judgment_angle_equal(1,BCD)", "isosceles_triangle_judgment_angle_equal(1,BDA)"]} | |
67 | XiaokaiZhang_2023-03-12 | Geometry3k-67 | 3 | 如图所示，QT=x，RQ=6，SQ=18，SR=14，∠TRQ=∠SRT。求x的值。 | As shown in the diagram, QT=x, RQ=6, SQ=18, SR=14, ∠TRQ=∠SRT. Find the value of x. | 67.png | [
"Shape(QT,TR,RQ)",
"Shape(TS,SR,RT)",
"Collinear(QTS)"
] | [
"Equal(LengthOfLine(QT),x)",
"Equal(LengthOfLine(RQ),6)",
"Equal(LengthOfLine(SQ),18)",
"Equal(LengthOfLine(SR),14)",
"Equal(MeasureOfAngle(TRQ),MeasureOfAngle(SRT))"
] | [
"Equal(LengthOfLine(QT),x)",
"Equal(LengthOfLine(RQ),6)",
"Equal(LengthOfLine(SQ),18)",
"Equal(LengthOfLine(SR),14)",
"Equal(MeasureOfAngle(TRQ),MeasureOfAngle(SRT))"
] | Value(x) | 27/5 | [
"line_addition(1,QT,TS)",
"bisector_of_angle_judgment_angle_equal(1,RT,SRQ)",
"bisector_of_angle_property_line_ratio(1,RT,SRQ)"
] | {"START": ["line_addition(1,QT,TS)", "bisector_of_angle_judgment_angle_equal(1,RT,SRQ)"], "bisector_of_angle_judgment_angle_equal(1,RT,SRQ)": ["bisector_of_angle_property_line_ratio(1,RT,SRQ)"]} | |
68 | XiaokaiZhang_2023-03-12 | Geometry3k-68 | 6 | 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。 | 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. | 68.png | [
"Shape(AC,CD,DA)",
"Shape(DC,CB,BD)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(AD),5)",
"Equal(LengthOfLine(BC),32)",
"Equal(LengthOfLine(CD),12)",
"PerpendicularBetweenLine(AC,BC)",
"PerpendicularBetweenLine(BD,CD)",
"SimilarBetweenTriangle(ACB,CDB)"
] | [
"PerpendicularBetweenLine(AC,BC)",
"PerpendicularBetweenLine(BD,CD)"
] | Value(PerimeterOfTriangle(ACB)) | sqrt(1193)+45 | [
"adjacent_complementary_angle(1,BDC,CDA)",
"right_triangle_judgment_angle(1,CDA)",
"right_triangle_judgment_angle(1,ACB)",
"right_triangle_property_pythagorean(1,CDA)",
"right_triangle_property_pythagorean(1,ACB)",
"triangle_perimeter_formula(1,ACB)"
] | {"START": ["adjacent_complementary_angle(1,BDC,CDA)", "right_triangle_judgment_angle(1,ACB)", "triangle_perimeter_formula(1,ACB)"], "adjacent_complementary_angle(1,BDC,CDA)": ["right_triangle_judgment_angle(1,CDA)"], "right_triangle_judgment_angle(1,ACB)": ["right_triangle_property_pythagorean(1,ACB)"], "right_triangle_judgment_angle(1,CDA)": ["right_triangle_property_pythagorean(1,CDA)"]} | |
69 | XiaokaiZhang_2023-03-12 | Geometry3k-69 | 2 | 如图所示，∠DEF=25°，∠GFD=65°，EG垂直于DG。求∠FDG的大小。 | As shown in the diagram, ∠DEF=25°, ∠GFD=65°, EG⊥DG. Find the measure of ∠FDG. | 69.png | [
"Shape(DE,EG,GD)",
"Shape(DG,GF,FD)",
"Collinear(EGF)"
] | [
"Equal(MeasureOfAngle(DEF),25)",
"Equal(MeasureOfAngle(GFD),65)",
"PerpendicularBetweenLine(EG,DG)"
] | [
"Equal(MeasureOfAngle(DEF),25)",
"Equal(MeasureOfAngle(GFD),65)",
"PerpendicularBetweenLine(EG,DG)"
] | Value(MeasureOfAngle(FDG)) | 25 | [
"adjacent_complementary_angle(1,EGD,DGF)",
"triangle_property_angle_sum(1,DGF)"
] | {"START": ["adjacent_complementary_angle(1,EGD,DGF)", "triangle_property_angle_sum(1,DGF)"]} | |
70 | XiaokaiZhang_2023-04-02 | Geometry3k-70 | 3 | 如图所示，JK=12，LK=2，ML=x，MN=6。求x的值。 | As shown in the diagram, JK=12, LK=2, ML=x, MN=6. Find the value of x. | 70.png | [
"Shape(AKJ,JK)",
"Shape(KJ,AJN,NM,AMK)",
"Shape(AMK,ML,LK)",
"Shape(ANM,MN)",
"Collinear(LKJ)",
"Collinear(LMN)",
"Cocircular(A,KJNM)"
] | [
"Equal(LengthOfLine(JK),12)",
"Equal(LengthOfLine(LK),2)",
"Equal(LengthOfLine(ML),x)",
"Equal(LengthOfLine(MN),6)"
] | [
"Equal(LengthOfLine(JK),12)",
"Equal(LengthOfLine(LK),2)",
"Equal(LengthOfLine(ML),x)",
"Equal(LengthOfLine(MN),6)"
] | Value(x) | -3+sqrt(37) | [
"circle_property_circular_power_segment_and_segment_line(1,LKJ,LMN,A)",
"line_addition(1,LK,KJ)",
"line_addition(1,LM,MN)"
] | {"START": ["circle_property_circular_power_segment_and_segment_line(1,LKJ,LMN,A)", "line_addition(1,LK,KJ)", "line_addition(1,LM,MN)"]} | |
71 | XiaokaiZhang_2023-03-12 | Geometry3k-71 | 1 | 如图所示，∠FHE=15*x°，三角形EFG为等边三角形，EH平分∠GEF。求x的值。 | As shown in the diagram, ∠FHE=15*x°, △EFG is an equilateral △, EH is the angle bisector of ∠GEF. Find the value of x. | 71.png | [
"Shape(EF,FH,HE)",
"Shape(EH,HG,GE)",
"Collinear(FHG)"
] | [
"Equal(MeasureOfAngle(FHE),15*x)",
"EquilateralTriangle(EFG)",
"IsBisectorOfAngle(EH,GEF)"
] | [
"Equal(MeasureOfAngle(FHE),15*x)"
] | Value(x) | 6 | [
"isosceles_triangle_property_line_coincidence(3,EFG,H)"
] | {"START": ["isosceles_triangle_property_line_coincidence(3,EFG,H)"]} | |
72 | XiaokaiZhang_2023-04-02 | Geometry3k-72 | 4 | 如图所示，∠TYZ=52°，∠ZYX=38°，TY垂直于XY，XW垂直于TW，YX⊥WX，YZ垂直于TZ。求∠WTZ的大小。 | As shown in the diagram, ∠TYZ=52°, ∠ZYX=38°, TY is perpendicular to XY, XW is perpendicular to TW, YX⊥WX, YZ is perpendicular to TZ. Find the measure of ∠WTZ. | 72.png | [
"Shape(TY,YZ,ZT)",
"Shape(TZ,ZW,WT)",
"Shape(ZY,YX,XW,WZ)",
"Collinear(YZW)"
] | [
"Equal(MeasureOfAngle(TYZ),52)",
"Equal(MeasureOfAngle(ZYX),38)",
"PerpendicularBetweenLine(TY,XY)",
"PerpendicularBetweenLine(XW,TW)",
"PerpendicularBetweenLine(YX,WX)",
"PerpendicularBetweenLine(YZ,TZ)"
] | [
"Equal(MeasureOfAngle(TYZ),52)",
"Equal(MeasureOfAngle(ZYX),38)",
"PerpendicularBetweenLine(TY,XY)",
"PerpendicularBetweenLine(XW,TW)",
"PerpendicularBetweenLine(YX,WX)",
"PerpendicularBetweenLine(YZ,TZ)"
] | Value(MeasureOfAngle(WTZ)) | 52 | [
"triangle_property_angle_sum(1,WYX)",
"angle_addition(1,XWY,YWT)",
"adjacent_complementary_angle(1,YZT,TZW)",
"triangle_property_angle_sum(1,WTZ)"
] | {"START": ["triangle_property_angle_sum(1,WYX)", "angle_addition(1,XWY,YWT)", "adjacent_complementary_angle(1,YZT,TZW)", "triangle_property_angle_sum(1,WTZ)"]} | |
73 | XiaokaiZhang_2023-03-12 | Geometry3k-73 | 8 | 如图所示，PQ=y，QR=x，SP=2，SR=4，PQ⊥RQ，RS⊥QS。求y的值。 | As shown in the diagram, PQ=y, QR=x, SP=2, SR=4, PQ⊥RQ, RS is perpendicular to QS. Find the value of y. | 73.png | [
"Shape(RS,SQ,QR)",
"Shape(SP,PQ,QS)",
"Collinear(RSP)"
] | [
"Equal(LengthOfLine(PQ),y)",
"Equal(LengthOfLine(QR),x)",
"Equal(LengthOfLine(SP),2)",
"Equal(LengthOfLine(SR),4)",
"PerpendicularBetweenLine(PQ,RQ)",
"PerpendicularBetweenLine(RS,QS)"
] | [
"Equal(LengthOfLine(PQ),y)",
"Equal(LengthOfLine(QR),x)",
"Equal(LengthOfLine(SP),2)",
"Equal(LengthOfLine(SR),4)",
"PerpendicularBetweenLine(PQ,RQ)",
"PerpendicularBetweenLine(RS,QS)"
] | Value(y) | 2*sqrt(3) | [
"adjacent_complementary_angle(1,RSQ,QSP)",
"right_triangle_judgment_angle(1,RSQ)",
"right_triangle_judgment_angle(1,QSP)",
"right_triangle_judgment_angle(1,PQR)",
"right_triangle_property_pythagorean(1,RSQ)",
"right_triangle_property_pythagorean(1,QSP)",
"right_triangle_property_pythagorean(1,PQR)",
"... | {"START": ["adjacent_complementary_angle(1,RSQ,QSP)", "right_triangle_judgment_angle(1,RSQ)", "right_triangle_judgment_angle(1,PQR)", "line_addition(1,RS,SP)"], "adjacent_complementary_angle(1,RSQ,QSP)": ["right_triangle_judgment_angle(1,QSP)"], "right_triangle_judgment_angle(1,PQR)": ["right_triangle_property_pythagorean(1,PQR)"], "right_triangle_judgment_angle(1,QSP)": ["right_triangle_property_pythagorean(1,QSP)"], "right_triangle_judgment_angle(1,RSQ)": ["right_triangle_property_pythagorean(1,RSQ)"]} | |
74 | XiaokaiZhang_2023-04-02 | Geometry3k-74 | 3 | 如图所示，AB=y，AC=12，AD=BD，∠CAB=x°，DB垂直于CB，四边形ADBC是正方形。求x的值。 | As shown in the diagram, AB=y, AC=12, AD=BD, ∠CAB=x°, DB is perpendicular to CB, ADBC is a square. Find the value of x. | 74.png | [
"Shape(AD,DB,BA)",
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),12)",
"Equal(LengthOfLine(AD),LengthOfLine(BD))",
"Equal(MeasureOfAngle(CAB),x)",
"PerpendicularBetweenLine(DB,CB)",
"Square(ADBC)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),12)",
"Equal(LengthOfLine(AD),LengthOfLine(BD))",
"Equal(MeasureOfAngle(CAB),x)",
"PerpendicularBetweenLine(DB,CB)"
] | Value(x) | 45 | [
"isosceles_triangle_judgment_line_equal(1,CAB)",
"isosceles_triangle_property_angle_equal(1,CAB)",
"triangle_property_angle_sum(1,CAB)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,CAB)", "triangle_property_angle_sum(1,CAB)"], "isosceles_triangle_judgment_line_equal(1,CAB)": ["isosceles_triangle_property_angle_equal(1,CAB)"]} | |
75 | XiaokaiZhang_2023-03-12 | Geometry3k-76 | 4 | 如图所示，AN=10，BC=30，CN=5，AC⊥NC。求△ABC的面积。 | As shown in the diagram, AN=10, BC=30, CN=5, AC is perpendicular to NC. Find the area of △ABC. | 75.png | [
"Shape(AB,BC,CA)",
"Shape(AC,CN,NA)",
"Collinear(BCN)"
] | [
"Equal(LengthOfLine(AN),10)",
"Equal(LengthOfLine(BC),30)",
"Equal(LengthOfLine(CN),5)",
"PerpendicularBetweenLine(AC,NC)"
] | [
"Equal(LengthOfLine(AN),10)",
"Equal(LengthOfLine(BC),30)",
"Equal(LengthOfLine(CN),5)",
"PerpendicularBetweenLine(AC,NC)"
] | Value(AreaOfTriangle(ABC)) | 75*sqrt(3) | [
"adjacent_complementary_angle(1,BCA,ACN)",
"right_triangle_judgment_angle(1,ACN)",
"right_triangle_property_pythagorean(1,ACN)",
"triangle_area_formula_sine(1,CAB)"
] | {"START": ["adjacent_complementary_angle(1,BCA,ACN)", "right_triangle_judgment_angle(1,ACN)", "triangle_area_formula_sine(1,CAB)"], "right_triangle_judgment_angle(1,ACN)": ["right_triangle_property_pythagorean(1,ACN)"]} | |
76 | XiaokaiZhang_2023-04-02 | Geometry3k-77 | 1 | 如图所示，QT=5*y，RT=x，ST=2*y+12，TP=5*x-28，QR和PS是▱RQPS的一组对边。求x的值。 | As shown in the diagram, QT=5*y, RT=x, ST=2*y+12, TP=5*x-28, quadrilateral RQPS is a ▱. Find the value of x. | 76.png | [
"Shape(RQ,QT,TR)",
"Shape(TQ,QP,PT)",
"Shape(RT,TS,SR)",
"Shape(TP,PS,ST)",
"Collinear(RTP)",
"Collinear(QTS)"
] | [
"Equal(LengthOfLine(QT),5*y)",
"Equal(LengthOfLine(RT),x)",
"Equal(LengthOfLine(ST),2*y+12)",
"Equal(LengthOfLine(TP),5*x-28)",
"Parallelogram(RQPS)"
] | [
"Equal(LengthOfLine(QT),5*y)",
"Equal(LengthOfLine(RT),x)",
"Equal(LengthOfLine(ST),2*y+12)",
"Equal(LengthOfLine(TP),5*x-28)"
] | Value(x) | 7 | [
"parallelogram_property_diagonal_bisection(1,RQPS,T)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,RQPS,T)"]} | |
77 | XiaokaiZhang_2023-04-02 | Geometry3k-78 | 3 | 如图所示，∠BGE=x°，∠CGD=135°，∠DGB=145°，∠EGC=x°。求x的值。 | As shown in the diagram, ∠BGE=x°, ∠CGD=135°, ∠DGB=145°, ∠EGC=x°. Find the value of x. | 77.png | [
"Shape(GDC,CG,GD)",
"Shape(GCE,EG,GC)",
"Shape(GEB,BG,GE)",
"Shape(GBD,DG,GB)",
"Cocircular(G,DCEB)"
] | [
"Equal(MeasureOfAngle(BGE),x)",
"Equal(MeasureOfAngle(CGD),135)",
"Equal(MeasureOfAngle(DGB),145)",
"Equal(MeasureOfAngle(EGC),x)"
] | [
"Equal(MeasureOfAngle(BGE),x)",
"Equal(MeasureOfAngle(CGD),135)",
"Equal(MeasureOfAngle(DGB),145)",
"Equal(MeasureOfAngle(EGC),x)"
] | Value(x) | 40 | [
"angle_addition(1,CGD,DGB)",
"angle_addition(1,BGE,EGC)",
"round_angle(1,BGC,CGB)"
] | {"START": ["angle_addition(1,CGD,DGB)", "angle_addition(1,BGE,EGC)", "round_angle(1,BGC,CGB)"]} | |
78 | XiaokaiZhang_2023-04-02 | Geometry3k-79 | 1 | 如图所示，DE=6*x-12，FE=4*y，GD=6*y-42，GF=2*x+36，四边形EDGF是▱。求y的值。 | As shown in the diagram, DE=6*x-12, FE=4*y, GD=6*y-42, GF=2*x+36, EDGF is a ▱. Find the value of y. | 78.png | [
"Shape(ED,DG,GF,FE)"
] | [
"Equal(LengthOfLine(DE),6*x-12)",
"Equal(LengthOfLine(FE),4*y)",
"Equal(LengthOfLine(GD),6*y-42)",
"Equal(LengthOfLine(GF),2*x+36)",
"Parallelogram(EDGF)"
] | [
"Equal(LengthOfLine(DE),6*x-12)",
"Equal(LengthOfLine(FE),4*y)",
"Equal(LengthOfLine(GD),6*y-42)",
"Equal(LengthOfLine(GF),2*x+36)"
] | Value(y) | 21 | [
"parallelogram_property_opposite_line_equal(1,DGFE)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,DGFE)"]} | |
79 | XiaokaiZhang_2023-04-02 | Geometry3k-80 | 1 | 如图所示，BA=5，BC=12，DB=10，EB=x。求x的值。 | As shown in the diagram, BA=5, BC=12, DB=10, EB=x. Find the value of x. | 79.png | [
"Shape(ODA,AB,BD)",
"Shape(OAE,EB,BA)",
"Shape(OEC,CB,BE)",
"Shape(OCD,DB,BC)",
"Collinear(ABC)",
"Collinear(EBD)",
"Cocircular(O,AECD)"
] | [
"Equal(LengthOfLine(BA),5)",
"Equal(LengthOfLine(BC),12)",
"Equal(LengthOfLine(DB),10)",
"Equal(LengthOfLine(EB),x)"
] | [
"Equal(LengthOfLine(BA),5)",
"Equal(LengthOfLine(BC),12)",
"Equal(LengthOfLine(DB),10)",
"Equal(LengthOfLine(EB),x)"
] | Value(x) | 6 | [
"circle_property_circular_power_chord_and_chord(1,ABC,EBD,O)"
] | {"START": ["circle_property_circular_power_chord_and_chord(1,ABC,EBD,O)"]} | |
80 | XiaokaiZhang_2023-03-12 | Geometry3k-81 | 1 | 如图所示，BC=x，BQ=6，QC=8。求x的值。 | As shown in the diagram, BC=x, BQ=6, QC=8. Find the value of x. | 80.png | [
"Shape(AD,DB,BC,CA)",
"Shape(DQ,QB,BD)",
"Collinear(ADQ)",
"Collinear(QBC)"
] | [
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(BQ),6)",
"Equal(LengthOfLine(QC),8)"
] | [
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(BQ),6)",
"Equal(LengthOfLine(QC),8)"
] | Value(x) | 2 | [
"line_addition(1,QB,BC)"
] | {"START": ["line_addition(1,QB,BC)"]} | |
81 | XiaokaiZhang_2023-04-02 | Geometry3k-82 | 2 | 如图所示，∠DEF=5*x°，∠FDE=5*x°，∠GFE=9*x+7°。求∠GFE的大小。 | As shown in the diagram, ∠DEF=5*x°, ∠FDE=5*x°, ∠GFE=9*x+7°. Find the measure of ∠GFE. | 81.png | [
"Shape(GF,FE)",
"Shape(FD,DE,EF)",
"Collinear(GFD)"
] | [
"Equal(MeasureOfAngle(DEF),5*x)",
"Equal(MeasureOfAngle(FDE),5*x)",
"Equal(MeasureOfAngle(GFE),9*x+7)"
] | [
"Equal(MeasureOfAngle(DEF),5*x)",
"Equal(MeasureOfAngle(FDE),5*x)",
"Equal(MeasureOfAngle(GFE),9*x+7)"
] | Value(MeasureOfAngle(GFE)) | 70 | [
"adjacent_complementary_angle(1,GFE,EFD)",
"triangle_property_angle_sum(1,FDE)"
] | {"START": ["adjacent_complementary_angle(1,GFE,EFD)", "triangle_property_angle_sum(1,FDE)"]} | |
82 | XiaokaiZhang_2023-04-02 | Geometry3k-83 | 9 | 如图所示，AE=12，BE=12，CE=17，DE=17，DE垂直于AE。求四边形ADBC的面积。 | As shown in the diagram, AE=12, BE=12, CE=17, DE=17, DE⊥AE. Find the area of ADBC. | 82.png | [
"Shape(AD,DE,EA)",
"Shape(AE,EC,CA)",
"Shape(DB,BE,ED)",
"Shape(EB,BC,CE)",
"Collinear(DEC)",
"Collinear(AEB)"
] | [
"Equal(LengthOfLine(AE),12)",
"Equal(LengthOfLine(BE),12)",
"Equal(LengthOfLine(CE),17)",
"Equal(LengthOfLine(DE),17)",
"PerpendicularBetweenLine(DE,AE)"
] | [
"Equal(LengthOfLine(AE),12)",
"Equal(LengthOfLine(BE),12)",
"Equal(LengthOfLine(CE),17)",
"Equal(LengthOfLine(DE),17)",
"PerpendicularBetweenLine(DE,AE)"
] | Value(AreaOfQuadrilateral(ADBC)) | 408 | [
"perpendicular_bisector_judgment_per_and_mid(1,AE,DC)",
"perpendicular_bisector_property_distance_equal(1,AE,DC)",
"vertical_angle(1,DEA,CEB)",
"perpendicular_bisector_judgment_per_and_mid(1,BE,CD)",
"perpendicular_bisector_property_distance_equal(1,BE,CD)",
"kite_judgment_equal_and_equal(1,ADBC)",
"lin... | {"START": ["perpendicular_bisector_judgment_per_and_mid(1,AE,DC)", "vertical_angle(1,DEA,CEB)", "line_addition(1,DE,EC)", "line_addition(1,AE,EB)"], "kite_judgment_equal_and_equal(1,ADBC)": ["kite_area_formula_diagonal(1,ADBC)"], "perpendicular_bisector_judgment_per_and_mid(1,AE,DC)": ["perpendicular_bisector_property_distance_equal(1,AE,DC)", "perpendicular_bisector_judgment_per_and_mid(1,BE,CD)"], "perpendicular_bisector_judgment_per_and_mid(1,BE,CD)": ["perpendicular_bisector_property_distance_equal(1,BE,CD)"], "perpendicular_bisector_property_distance_equal(1,AE,DC)": ["kite_judgment_equal_and_equal(1,ADBC)"], "perpendicular_bisector_property_distance_equal(1,BE,CD)": ["kite_judgment_equal_and_equal(1,ADBC)"], "vertical_angle(1,DEA,CEB)": ["perpendicular_bisector_judgment_per_and_mid(1,BE,CD)"]} | |
83 | XiaokaiZhang_2023-04-02 | Geometry3k-84 | 0 | 如图所示，JL=y+4/5，LC=2*y-11/5，MI=12-3*x，TM=10-2*x，TM=MI，JT平行于LM，LM平行于CI。求x的值。 | As shown in the diagram, JL=y+4/5, LC=2*y-11/5, MI=12-3*x, TM=10-2*x, TM=MI, JT∥LM, LM∥CI. Find the value of x. | 83.png | [
"Shape(JL,LM,MT,TJ)",
"Shape(LC,CI,IM,ML)",
"Collinear(JLC)",
"Collinear(TMI)"
] | [
"Equal(LengthOfLine(JL),y+4/5)",
"Equal(LengthOfLine(LC),2*y-11/5)",
"Equal(LengthOfLine(MI),12-3*x)",
"Equal(LengthOfLine(TM),10-2*x)",
"Equal(LengthOfLine(TM),LengthOfLine(MI))",
"ParallelBetweenLine(JT,LM)",
"ParallelBetweenLine(LM,CI)"
] | [
"Equal(LengthOfLine(JL),y+4/5)",
"Equal(LengthOfLine(LC),2*y-11/5)",
"Equal(LengthOfLine(MI),12-3*x)",
"Equal(LengthOfLine(TM),10-2*x)",
"Equal(LengthOfLine(TM),LengthOfLine(MI))",
"ParallelBetweenLine(JT,LM)",
"ParallelBetweenLine(LM,CI)"
] | Value(x) | 2 | [] | {"START": []} | |
84 | XiaokaiZhang_2023-03-12 | Geometry3k-85 | 3 | 如图所示，AB=32，AD=DC，BC=2*x-3，EF=12，EH=HG，FG=x-5，∠BCD=∠FGH，∠DAB=∠HEF。求x的值。 | As shown in the diagram, AB=32, AD=DC, BC=2*x-3, EF=12, EH=HG, FG=x-5, ∠BCD=∠FGH, ∠DAB=∠HEF. Find the value of x. | 84.png | [
"Shape(EF,FH,HE)",
"Shape(HF,FG,GH)",
"Shape(AB,BD,DA)",
"Shape(DB,BC,CD)",
"Collinear(EHG)",
"Collinear(ADC)"
] | [
"Equal(LengthOfLine(AB),32)",
"Equal(LengthOfLine(AD),LengthOfLine(DC))",
"Equal(LengthOfLine(BC),2*x-3)",
"Equal(LengthOfLine(EF),12)",
"Equal(LengthOfLine(EH),LengthOfLine(HG))",
"Equal(LengthOfLine(FG),x-5)",
"Equal(MeasureOfAngle(BCD),MeasureOfAngle(FGH))",
"Equal(MeasureOfAngle(DAB),MeasureOfAngl... | [
"Equal(LengthOfLine(AB),32)",
"Equal(LengthOfLine(AD),LengthOfLine(DC))",
"Equal(LengthOfLine(BC),2*x-3)",
"Equal(LengthOfLine(EF),12)",
"Equal(LengthOfLine(EH),LengthOfLine(HG))",
"Equal(LengthOfLine(FG),x-5)",
"Equal(MeasureOfAngle(BCD),MeasureOfAngle(FGH))",
"Equal(MeasureOfAngle(DAB),MeasureOfAngl... | Value(x) | 31/2 | [
"similar_triangle_judgment_aa(1,FGE,BCA)",
"similar_triangle_property_line_ratio(1,EFG,ABC)",
"similar_triangle_property_line_ratio(1,GEF,CAB)"
] | {"START": ["similar_triangle_judgment_aa(1,FGE,BCA)"], "similar_triangle_judgment_aa(1,FGE,BCA)": ["similar_triangle_property_line_ratio(1,GEF,CAB)", "similar_triangle_property_line_ratio(1,EFG,ABC)"]} | |
85 | XiaokaiZhang_2023-04-02 | Geometry3k-86 | 0 | 如图所示，∠ABC=110°。求∠ABC的大小。 | As shown in the diagram, ∠ABC=110°. Find the measure of ∠ABC. | 85.png | [
"Shape(AB,BC)"
] | [
"Equal(MeasureOfAngle(ABC),110)"
] | [
"Equal(MeasureOfAngle(ABC),110)"
] | Value(MeasureOfAngle(ABC)) | 110 | [] | {"START": []} | |
86 | XiaokaiZhang_2023-04-02 | Geometry3k-87 | 5 | 如图所示，NP=2*x-30，NR=2*x+10，NMRQ是长方形。求直线MP的长度。 | As shown in the diagram, NP=2*x-30, NR=2*x+10, NMRQ is a rectangle. Find the length of line MP. | 86.png | [
"Shape(NM,MP,PN)",
"Shape(PM,MR,RP)",
"Shape(NP,PQ,QN)",
"Shape(QP,PR,RQ)",
"Collinear(NPR)",
"Collinear(MPQ)"
] | [
"Equal(LengthOfLine(NP),2*x-30)",
"Equal(LengthOfLine(NR),2*x+10)",
"Rectangle(NMRQ)"
] | [] | Value(LengthOfLine(MP)) | 40 | [
"parallelogram_property_diagonal_bisection(1,NMRQ,P)",
"line_addition(1,NP,PR)",
"parallelogram_property_diagonal_bisection(1,MRQN,P)",
"rectangle_property_diagonal_equal(1,NMRQ)",
"line_addition(1,MP,PQ)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,NMRQ,P)", "line_addition(1,NP,PR)", "parallelogram_property_diagonal_bisection(1,MRQN,P)", "rectangle_property_diagonal_equal(1,NMRQ)", "line_addition(1,MP,PQ)"]} | |
87 | XiaokaiZhang_2023-04-02 | Geometry3k-88 | 2 | 如图所示，BCAW的面积为500，BW=30，DG=15，BCAW与DEFG相似。求四边形DEFG的面积。 | As shown in the diagram, the area of BCAW is 500, BW=30, DG=15, quadrilateral BCAW is similar to quadrilateral DEFG. Find the area of DEFG. | 87.png | [
"Shape(BC,CA,AW,WB)",
"Shape(DE,EF,FG,GD)"
] | [
"Equal(AreaOfQuadrilateral(BCAW),500)",
"Equal(LengthOfLine(BW),30)",
"Equal(LengthOfLine(DG),15)",
"SimilarBetweenQuadrilateral(BCAW,DEFG)"
] | [
"Equal(AreaOfQuadrilateral(BCAW),500)",
"Equal(LengthOfLine(BW),30)",
"Equal(LengthOfLine(DG),15)"
] | Value(AreaOfQuadrilateral(DEFG)) | 125 | [
"similar_quadrilateral_property_line_ratio(1,WBCA,GDEF)",
"similar_quadrilateral_property_area_square_ratio(1,BCAW,DEFG)"
] | {"START": ["similar_quadrilateral_property_line_ratio(1,WBCA,GDEF)", "similar_quadrilateral_property_area_square_ratio(1,BCAW,DEFG)"]} | |
88 | XiaokaiZhang_2023-04-02 | Geometry3k-89 | 3 | 如图所示，SR=TS，∠TAS=93°，弧ARS的角度为x，⊙A的圆心为A。求x的值。 | As shown in the diagram, SR=TS, ∠TAS=93°, the measure of arc ARS is x, the center of ⊙A is A. Find the value of x. | 88.png | [
"Shape(ATR,RS,SA,AT)",
"Shape(ARS,SR)",
"Shape(AS,ST,TA)",
"Shape(AST,TS)",
"Cocircular(A,RST)"
] | [
"Equal(LengthOfLine(SR),LengthOfLine(TS))",
"Equal(MeasureOfAngle(TAS),93)",
"Equal(MeasureOfArc(ARS),x)",
"IsCentreOfCircle(A,A)"
] | [
"Equal(LengthOfLine(SR),LengthOfLine(TS))",
"Equal(MeasureOfAngle(TAS),93)",
"Equal(MeasureOfArc(ARS),x)",
"IsCentreOfCircle(A,A)"
] | Value(x) | 93 | [
"congruent_arc_judgment_chord_equal(1,ARS,AST)",
"congruent_arc_property_measure_equal(1,ARS,AST)",
"arc_property_center_angle(1,AST,A)"
] | {"START": ["congruent_arc_judgment_chord_equal(1,ARS,AST)", "arc_property_center_angle(1,AST,A)"], "congruent_arc_judgment_chord_equal(1,ARS,AST)": ["congruent_arc_property_measure_equal(1,ARS,AST)"]} | |
89 | XiaokaiZhang_2023-04-02 | Geometry3k-90 | 1 | 如图所示，∠DGH=64°，IL∥BN，WJ∥AK。求∠JGD的大小。 | As shown in the diagram, ∠DGH=64°, IL is parallel to BN, WJ∥AK. Find the measure of ∠JGD. | 89.png | [
"Shape(AB,BC)",
"Shape(CB,BD)",
"Shape(BD,DE)",
"Shape(ED,DF)",
"Shape(FD,DG)",
"Shape(DG,GH)",
"Shape(HG,GI)",
"Shape(IG,GJ)",
"Shape(GJ,JK)",
"Shape(KJ,JL)",
"Shape(LJ,JB)",
"Shape(JB,BA)",
"Shape(BJ,JG,GD,DB)",
"Collinear(ABDF)",
"Collinear(LJGH)",
"Collinear(CBJK)",
"Collinear(ED... | [
"Equal(MeasureOfAngle(DGH),64)",
"ParallelBetweenLine(IL,BN)",
"ParallelBetweenLine(WJ,AK)"
] | [
"Equal(MeasureOfAngle(DGH),64)",
"ParallelBetweenLine(IL,BN)",
"ParallelBetweenLine(WJ,AK)"
] | Value(MeasureOfAngle(JGD)) | 116 | [
"adjacent_complementary_angle(1,JGD,DGH)"
] | {"START": ["adjacent_complementary_angle(1,JGD,DGH)"]} | |
90 | XiaokaiZhang_2023-03-12 | Geometry3k-91 | 3 | 如图所示，BA=3，BD=x-1，CE=x+2，EF=8，∠GAB=∠EFG，AB⊥CB，DE垂直于FE。求直线BD的长度。 | As shown in the diagram, BA=3, BD=x-1, CE=x+2, EF=8, ∠GAB=∠EFG, AB is perpendicular to CB, DE is perpendicular to FE. Find the length of line BD. | 90.png | [
"Shape(AB,BC,CG,GA)",
"Shape(GC,CD,DG)",
"Shape(GD,DE,EF,FG)",
"Collinear(AGD)",
"Collinear(CGF)",
"Collinear(BCDE)"
] | [
"Equal(LengthOfLine(BA),3)",
"Equal(LengthOfLine(BD),x-1)",
"Equal(LengthOfLine(CE),x+2)",
"Equal(LengthOfLine(EF),8)",
"Equal(MeasureOfAngle(GAB),MeasureOfAngle(EFG))",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(DE,FE)"
] | [
"Equal(LengthOfLine(BA),3)",
"Equal(LengthOfLine(BD),x-1)",
"Equal(LengthOfLine(CE),x+2)",
"Equal(LengthOfLine(EF),8)",
"Equal(MeasureOfAngle(GAB),MeasureOfAngle(EFG))",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(DE,FE)"
] | Value(LengthOfLine(BD)) | 9/5 | [
"mirror_similar_triangle_judgment_aa(1,DAB,CEF)",
"mirror_similar_triangle_property_line_ratio(1,DAB,CEF)",
"mirror_similar_triangle_property_line_ratio(1,ABD,FCE)"
] | {"START": ["mirror_similar_triangle_judgment_aa(1,DAB,CEF)"], "mirror_similar_triangle_judgment_aa(1,DAB,CEF)": ["mirror_similar_triangle_property_line_ratio(1,DAB,CEF)", "mirror_similar_triangle_property_line_ratio(1,ABD,FCE)"]} | |
91 | XiaokaiZhang_2023-03-12 | Geometry3k-92 | 1 | 如图所示，WX=a+12，WZ=4*a-15，XY=YZ，WY垂直平分AB。求直线WX的长度。 | As shown in the diagram, WX=a+12, WZ=4*a-15, XY=YZ, WY is the perpendicular bisector of ZX. Find the length of line WX. | 91.png | [
"Shape(WZ,ZY,YW)",
"Shape(WY,YX,XW)",
"Collinear(ZYX)"
] | [
"Equal(LengthOfLine(WX),a+12)",
"Equal(LengthOfLine(WZ),4*a-15)",
"Equal(LengthOfLine(XY),LengthOfLine(YZ))",
"IsPerpendicularBisectorOfLine(WY,ZX)"
] | [
"Equal(LengthOfLine(XY),LengthOfLine(YZ))"
] | Value(LengthOfLine(WX)) | 21 | [
"perpendicular_bisector_property_distance_equal(1,WY,ZX)"
] | {"START": ["perpendicular_bisector_property_distance_equal(1,WY,ZX)"]} | |
92 | XiaokaiZhang_2023-04-02 | Geometry3k-93 | 3 | 如图所示，BC=y，BD=12，CD=12，∠CBD=x°，BD⊥CD。求x的值。 | As shown in the diagram, BC=y, BD=12, CD=12, ∠CBD=x°, BD⊥CD. Find the value of x. | 92.png | [
"Shape(AB,BC,CA)",
"Shape(CB,BD,DC)"
] | [
"Equal(LengthOfLine(BC),y)",
"Equal(LengthOfLine(BD),12)",
"Equal(LengthOfLine(CD),12)",
"Equal(MeasureOfAngle(CBD),x)",
"PerpendicularBetweenLine(BD,CD)"
] | [
"Equal(LengthOfLine(BC),y)",
"Equal(LengthOfLine(BD),12)",
"Equal(LengthOfLine(CD),12)",
"Equal(MeasureOfAngle(CBD),x)",
"PerpendicularBetweenLine(BD,CD)"
] | Value(x) | 45 | [
"isosceles_triangle_judgment_line_equal(1,DCB)",
"isosceles_triangle_property_angle_equal(1,DCB)",
"triangle_property_angle_sum(1,DCB)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,DCB)", "triangle_property_angle_sum(1,DCB)"], "isosceles_triangle_judgment_line_equal(1,DCB)": ["isosceles_triangle_property_angle_equal(1,DCB)"]} | |
93 | XiaokaiZhang_2023-04-02 | Geometry3k-94 | 1 | 如图所示，∠DHB=38°，∠FDA=52°，HB垂直于DB。求∠HDF的大小。 | As shown in the diagram, ∠DHB=38°, ∠FDA=52°, HB is perpendicular to DB. Find the measure of ∠HDF. | 93.png | [
"Shape(CH,HI)",
"Shape(IH,HD)",
"Shape(HD,DF)",
"Shape(FD,DA)",
"Shape(AD,DB)",
"Shape(DB,BE)",
"Shape(EB,BG)",
"Shape(GB,BH)",
"Shape(BH,HC)",
"Shape(HB,BD,DH)",
"Collinear(CHDA)",
"Collinear(IHBE)",
"Collinear(GBDF)"
] | [
"Equal(MeasureOfAngle(DHB),38)",
"Equal(MeasureOfAngle(FDA),52)",
"PerpendicularBetweenLine(HB,DB)"
] | [
"Equal(MeasureOfAngle(DHB),38)",
"Equal(MeasureOfAngle(FDA),52)",
"PerpendicularBetweenLine(HB,DB)"
] | Value(MeasureOfAngle(HDF)) | 128 | [
"adjacent_complementary_angle(1,HDF,FDA)"
] | {"START": ["adjacent_complementary_angle(1,HDF,FDA)"]} | |
94 | XiaokaiZhang_2023-04-02 | Geometry3k-95 | 13 | 如图所示，⌒DBC的角度为170，D是圆D的圆心。求∠CAB的大小。 | As shown in the diagram, the measure of arc DBC is 170, D is the center of circle D. Find the measure of ∠CAB. | 94.png | [
"Shape(DCA,AC)",
"Shape(DC,CA,AD)",
"Shape(DA,AB,BD)",
"Shape(DAB,BA)",
"Shape(DB,DBC,CD)",
"Cocircular(D,CAB)"
] | [
"Equal(MeasureOfArc(DBC),170)",
"IsCentreOfCircle(D,D)"
] | [
"Equal(MeasureOfArc(DBC),170)",
"IsCentreOfCircle(D,D)"
] | Value(MeasureOfAngle(CAB)) | 85 | [
"arc_property_center_angle(1,DBC,D)",
"round_angle(1,CDB,BDC)",
"radius_of_circle_property_length_equal(1,DC,D)",
"radius_of_circle_property_length_equal(1,DA,D)",
"radius_of_circle_property_length_equal(1,DB,D)",
"isosceles_triangle_judgment_line_equal(1,DCA)",
"isosceles_triangle_property_angle_equal(... | {"START": ["arc_property_center_angle(1,DBC,D)", "round_angle(1,CDB,BDC)", "radius_of_circle_property_length_equal(1,DC,D)", "radius_of_circle_property_length_equal(1,DA,D)", "radius_of_circle_property_length_equal(1,DB,D)", "angle_addition(1,CAD,DAB)", "angle_addition(1,BDA,ADC)", "triangle_property_angle_sum(1,DCA)", "triangle_property_angle_sum(1,DAB)"], "isosceles_triangle_judgment_line_equal(1,DAB)": ["isosceles_triangle_property_angle_equal(1,DAB)"], "isosceles_triangle_judgment_line_equal(1,DCA)": ["isosceles_triangle_property_angle_equal(1,DCA)"], "radius_of_circle_property_length_equal(1,DA,D)": ["isosceles_triangle_judgment_line_equal(1,DCA)", "isosceles_triangle_judgment_line_equal(1,DAB)"], "radius_of_circle_property_length_equal(1,DB,D)": ["isosceles_triangle_judgment_line_equal(1,DAB)"], "radius_of_circle_property_length_equal(1,DC,D)": ["isosceles_triangle_judgment_line_equal(1,DCA)"]} | |
95 | XiaokaiZhang_2023-04-02 | Geometry3k-96 | 1 | 如图所示，∠PNO=56°，弧BMN的角度为70。求弧BOP的角度。 | As shown in the diagram, ∠PNO=56°, the measure of arc BMN is 70. Find the measure of arc BOP. | 95.png | [
"Shape(BPM,MP)",
"Shape(BMN,NP,PM)",
"Shape(PN,NO,BOP)",
"Shape(BNO,ON)",
"Cocircular(B,PMNO)"
] | [
"Equal(MeasureOfAngle(PNO),56)",
"Equal(MeasureOfArc(BMN),70)"
] | [
"Equal(MeasureOfAngle(PNO),56)",
"Equal(MeasureOfArc(BMN),70)"
] | Value(MeasureOfArc(BOP)) | 112 | [
"arc_property_circumference_angle_external(1,BOP,N)"
] | {"START": ["arc_property_circumference_angle_external(1,BOP,N)"]} | |
96 | XiaokaiZhang_2023-04-02 | Geometry3k-97 | 1 | 如图所示，∠ACB=3*y+36°，∠BDA=9*y-12°，∠CBD=12*x+72°，∠DAC=25*x+20°，四边形BDAC是平行四边形。求x的值。 | As shown in the diagram, ∠ACB=3*y+36°, ∠BDA=9*y-12°, ∠CBD=12*x+72°, ∠DAC=25*x+20°, BC and DA are opposite sides of the ▱ BDAC. Find the value of x. | 96.png | [
"Shape(BD,DA,AC,CB)"
] | [
"Equal(MeasureOfAngle(ACB),3*y+36)",
"Equal(MeasureOfAngle(BDA),9*y-12)",
"Equal(MeasureOfAngle(CBD),12*x+72)",
"Equal(MeasureOfAngle(DAC),25*x+20)",
"Parallelogram(BDAC)"
] | [
"Equal(MeasureOfAngle(ACB),3*y+36)",
"Equal(MeasureOfAngle(BDA),9*y-12)",
"Equal(MeasureOfAngle(CBD),12*x+72)",
"Equal(MeasureOfAngle(DAC),25*x+20)"
] | Value(x) | 4 | [
"parallelogram_property_opposite_angle_equal(1,BDAC)"
] | {"START": ["parallelogram_property_opposite_angle_equal(1,BDAC)"]} | |
97 | XiaokaiZhang_2023-04-02 | Geometry3k-98 | 1 | 如图所示，AD=11，BC=25，四边形BACD是风筝形。求BACD的面积。 | As shown in the diagram, AD=11, BC=25, BACD is a kite. Find the area of BACD. | 97.png | [
"Shape(BA,AO,OB)",
"Shape(BO,OD,DB)",
"Shape(AC,CO,OA)",
"Shape(OC,CD,DO)",
"Collinear(COB)",
"Collinear(AOD)"
] | [
"Equal(LengthOfLine(AD),11)",
"Equal(LengthOfLine(BC),25)",
"Kite(BACD)"
] | [
"Equal(LengthOfLine(AD),11)",
"Equal(LengthOfLine(BC),25)"
] | Value(AreaOfQuadrilateral(BACD)) | 275/2 | [
"kite_area_formula_diagonal(1,BACD)"
] | {"START": ["kite_area_formula_diagonal(1,BACD)"]} | |
98 | XiaokaiZhang_2023-04-02 | Geometry3k-99 | 4 | 如图所示，∠CBD=55°，∠FBG=35°，圆B的圆心为B。求⌒BFA的角度。 | As shown in the diagram, ∠CBD=55°, ∠FBG=35°, B is the center of ⊙B. Find the measure of arc BFA. | 98.png | [
"Shape(BCA,AB,BC)",
"Shape(BAG,GB,BA)",
"Shape(BGF,FB,BG)",
"Shape(BFD,DB,BF)",
"Shape(BDC,CB,BD)",
"Collinear(ABD)",
"Collinear(CBG)",
"Cocircular(B,CAGFD)"
] | [
"Equal(MeasureOfAngle(CBD),55)",
"Equal(MeasureOfAngle(FBG),35)",
"IsCentreOfCircle(B,B)"
] | [
"Equal(MeasureOfAngle(CBD),55)",
"Equal(MeasureOfAngle(FBG),35)",
"IsCentreOfCircle(B,B)"
] | Value(MeasureOfArc(BFA)) | 270 | [
"vertical_angle(1,CBD,GBA)",
"angle_addition(1,FBG,GBA)",
"round_angle(1,FBA,ABF)",
"arc_property_center_angle(1,BFA,B)"
] | {"START": ["vertical_angle(1,CBD,GBA)", "angle_addition(1,FBG,GBA)", "round_angle(1,FBA,ABF)", "arc_property_center_angle(1,BFA,B)"]} | |
99 | XiaokaiZhang_2023-03-12 | Geometry3k-100 | 3 | 如图所示，PQ=25*sqrt(3)，RQ=25，PQ垂直于RQ。求∠QRP的大小。 | As shown in the diagram, PQ=25*sqrt(3), RQ=25, PQ⊥RQ. Find the measure of ∠QRP. | 99.png | [
"Shape(PQ,QR,RP)"
] | [
"Equal(LengthOfLine(PQ),25*sqrt(3))",
"Equal(LengthOfLine(RQ),25)",
"PerpendicularBetweenLine(PQ,RQ)"
] | [
"Equal(LengthOfLine(PQ),25*sqrt(3))",
"Equal(LengthOfLine(RQ),25)",
"PerpendicularBetweenLine(PQ,RQ)"
] | Value(MeasureOfAngle(QRP)) | 60 | [
"right_triangle_judgment_angle(1,PQR)",
"right_triangle_property_pythagorean(1,PQR)",
"cosine_theorem(1,RPQ)"
] | {"START": ["right_triangle_judgment_angle(1,PQR)", "cosine_theorem(1,RPQ)"], "right_triangle_judgment_angle(1,PQR)": ["right_triangle_property_pythagorean(1,PQR)"]} | |
100 | XiaokaiZhang_2023-03-12 | Geometry3k-101 | 8 | 如图所示，AB=z，AN=x，AY=5，YB=14，YN=y，BA垂直于YA，YN垂直于AN。求y的值。 | As shown in the diagram, AB=z, AN=x, AY=5, YB=14, YN=y, BA⊥YA, YN is perpendicular to AN. Find the value of y. | 100.png | [
"Shape(AY,YN,NA)",
"Shape(AN,NB,BA)",
"Collinear(YNB)"
] | [
"Equal(LengthOfLine(AB),z)",
"Equal(LengthOfLine(AN),x)",
"Equal(LengthOfLine(AY),5)",
"Equal(LengthOfLine(YB),14)",
"Equal(LengthOfLine(YN),y)",
"PerpendicularBetweenLine(BA,YA)",
"PerpendicularBetweenLine(YN,AN)"
] | [
"Equal(LengthOfLine(AB),z)",
"Equal(LengthOfLine(AN),x)",
"Equal(LengthOfLine(AY),5)",
"Equal(LengthOfLine(YB),14)",
"Equal(LengthOfLine(YN),y)",
"PerpendicularBetweenLine(BA,YA)",
"PerpendicularBetweenLine(YN,AN)"
] | Value(y) | 25/14 | [
"adjacent_complementary_angle(1,YNA,ANB)",
"line_addition(1,YN,NB)",
"right_triangle_judgment_angle(1,YNA)",
"right_triangle_judgment_angle(1,ANB)",
"right_triangle_judgment_angle(1,BAY)",
"right_triangle_property_pythagorean(1,YNA)",
"right_triangle_property_pythagorean(1,ANB)",
"right_triangle_prope... | {"START": ["adjacent_complementary_angle(1,YNA,ANB)", "line_addition(1,YN,NB)", "right_triangle_judgment_angle(1,YNA)", "right_triangle_judgment_angle(1,BAY)"], "adjacent_complementary_angle(1,YNA,ANB)": ["right_triangle_judgment_angle(1,ANB)"], "right_triangle_judgment_angle(1,ANB)": ["right_triangle_property_pythagorean(1,ANB)"], "right_triangle_judgment_angle(1,BAY)": ["right_triangle_property_pythagorean(1,BAY)"], "right_triangle_judgment_angle(1,YNA)": ["right_triangle_property_pythagorean(1,YNA)"]} |
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