SunnyLin/FormalGeo7k_v1 huggingface dataset:
Problem: As shown in the diagram, the area of quadrilateral OLAB is 96, LE=7, OE=EA, OE=x, OL=LA, quadrilateral LABO is a rhombus. Find the value of x.
问题：如图所示，OLAB的面积为96，LE=7，OE=EA，OE=x，OL=LA，四边形LABO是菱形。求x的值。
Construction (CDL):
Shape(OL,LE,EO)
Shape(EL,LA,AE)
Shape(EA,AB,BE)
Shape(OE,EB,BO)
Collinear(OEA)
Collinear(LEB)
Conditions (CDL):
Equal(AreaOfQuadrilateral(OLAB),96)
Equal(LengthOfLine(LE),7)
Equal(LengthOfLine(OE),LengthOfLine(EA))
Equal(LengthOfLine(OE),x)
Equal(LengthOfLine(OL),LengthOfLine(LA))
Rhombus(LABO)
Goal: Value(x)
Answer: 48/7
Theorem sequence:
parallelogram_property_diagonal_bisection(1,LABO,E)
kite_area_formula_diagonal(1,LABO)
line_addition(1,LE,EB)
line_addition(1,OE,EA)
Problem: As shown in the diagram, BA=c, BC=a, BE=x, CA=b, EA=y, ∠ABC=60°, ∠CAB=30°, a=10*sqrt(3), AE is perpendicular to CE, BC is perpendicular to AC. Find the value of y.
问题：如图所示，BA=c，BC=a，BE=x，CA=b，EA=y，∠ABC=60°，∠CAB=30°，a=10*sqrt(3)，AE垂直于CE，BC垂直于AC。求y的值。
Construction (CDL):
Shape(BC,CE,EB)
Shape(EC,CA,AE)
Collinear(BEA)
Conditions (CDL):
Equal(LengthOfLine(BA),c)
Equal(LengthOfLine(BC),a)
Equal(LengthOfLine(BE),x)
Equal(LengthOfLine(CA),b)
Equal(LengthOfLine(EA),y)
Equal(MeasureOfAngle(ABC),60)
Equal(MeasureOfAngle(CAB),30)
Equal(a,10*sqrt(3))
PerpendicularBetweenLine(AE,CE)
PerpendicularBetweenLine(BC,AC)
Goal: Value(y)
Answer: 15*sqrt(3)
Theorem sequence:
adjacent_complementary_angle(1,AEC,CEB)
triangle_property_angle_sum(1,AEC)
sine_theorem(1,AEC)
sine_theorem(1,CAE)
sine_theorem(1,CEB)
Problem: As shown in the diagram, triangle ACB is congruent to triangle FHG, AB=13, AC=2*x+5, BC=7, FG=4*x+1, FH=11, HG=3*x-2. Find the value of x.
问题：如图所示，三角形ACB全等于三角形FHG，AB=13，AC=2*x+5，BC=7，FG=4*x+1，FH=11，HG=3*x-2。求x的值。
Construction (CDL):
Shape(BA,AC,CB)
Shape(FH,HG,GF)
Conditions (CDL):
CongruentBetweenTriangle(ACB,FHG)
Equal(LengthOfLine(AB),13)
Equal(LengthOfLine(AC),2*x+5)
Equal(LengthOfLine(BC),7)
Equal(LengthOfLine(FG),4*x+1)
Equal(LengthOfLine(FH),11)
Equal(LengthOfLine(HG),3*x-2)
Goal: Value(x)
Answer: 3
Theorem sequence:
congruent_triangle_property_line_equal(1,CBA,HGF)
Problem: As shown in the diagram, AC=y, AN=x, BA=z, NB=12, NC=8, BA is perpendicular to NA, NC is perpendicular to AC. Find the value of z.
问题：如图所示，AC=y，AN=x，BA=z，NB=12，NC=8，BA⊥NA，NC垂直于AC。求z的值。
Construction (CDL):
Shape(BA,AC,CB)
Shape(CA,AN,NC)
Collinear(NCB)
Conditions (CDL):
Equal(LengthOfLine(AC),y)
Equal(LengthOfLine(AN),x)
Equal(LengthOfLine(BA),z)
Equal(LengthOfLine(NB),12)
Equal(LengthOfLine(NC),8)
PerpendicularBetweenLine(BA,NA)
PerpendicularBetweenLine(NC,AC)
Goal: Value(z)
Answer: 4*sqrt(3)
Theorem sequence:
adjacent_complementary_angle(1,NCA,ACB)
right_triangle_judgment_angle(1,ACB)
right_triangle_judgment_angle(1,NCA)
right_triangle_judgment_angle(1,BAN)
right_triangle_property_pythagorean(1,ACB)
right_triangle_property_pythagorean(1,NCA)
right_triangle_property_pythagorean(1,BAN)
line_addition(1,NC,CB)
Problem: As shown in the diagram, AB=3*y-8, CB=2*x+7, DA=13, DC=10, ∠ADF=59°, ∠BFC=49°, ∠FBA=20°, ADCB is a ▱. Find the measure of ∠CAD.
问题：如图所示，AB=3*y-8，CB=2*x+7，DA=13，DC=10，∠ADF=59°，∠BFC=49°，∠FBA=20°，DA和CB是▱ADCB的一组对边。求∠CAD的大小。
Construction (CDL):
Shape(AD,DF,FA)
Shape(FD,DC,CF)
Shape(FC,CB,BF)
Shape(AF,FB,BA)
Collinear(AFC)
Collinear(DFB)
Conditions (CDL):
Equal(LengthOfLine(AB),3*y-8)
Equal(LengthOfLine(CB),2*x+7)
Equal(LengthOfLine(DA),13)
Equal(LengthOfLine(DC),10)
Equal(MeasureOfAngle(ADF),59)
Equal(MeasureOfAngle(BFC),49)
Equal(MeasureOfAngle(FBA),20)
Parallelogram(ADCB)
Goal: Value(MeasureOfAngle(CAD))
Answer: 72
Theorem sequence:
vertical_angle(1,DFA,BFC)
triangle_property_angle_sum(1,ADF)
Problem: As shown in the diagram, AX=5, YA=8, quadrilateral WZYX is a kite. Find the length of line YZ.
问题：如图所示，AX=5，YA=8，YZ和YX是风筝形WZYX的一组临边。求直线YZ的长度。
Construction (CDL):
Shape(WZ,ZA,AW)
Shape(AZ,ZY,YA)
Shape(AY,YX,XA)
Shape(WA,AX,XW)
Collinear(WAY)
Collinear(ZAX)
Conditions (CDL):
Equal(LengthOfLine(AX),5)
Equal(LengthOfLine(YA),8)
Kite(WZYX)
Goal: Value(LengthOfLine(YZ))
Answer: sqrt(89)
Theorem sequence:
kite_property_diagonal_perpendicular_bisection(1,YXWZ,A)
right_triangle_judgment_angle(1,YAZ)
right_triangle_property_pythagorean(1,YAZ)
Problem: As shown in the diagram, AB=19, AC=x, ∠ABC=24°, CA⊥BA. Find the value of x.
问题：如图所示，AB=19，AC=x，∠ABC=24°，CA⊥BA。求x的值。
Construction (CDL):
Shape(CA,AB,BC)
Conditions (CDL):
Equal(LengthOfLine(AB),19)
Equal(LengthOfLine(AC),x)
Equal(MeasureOfAngle(ABC),24)
PerpendicularBetweenLine(CA,BA)
Goal: Value(x)
Answer: 19*(-2*sqrt(5-sqrt(5))+sqrt(6)+sqrt(30))/(sqrt(2)+sqrt(10)+2*sqrt(3)*sqrt(5-sqrt(5)))
Theorem sequence:
triangle_property_angle_sum(1,CAB)
sine_theorem(1,ABC)
Problem: As shown in the diagram, BM=16, GC=x, MH=22, VG=12, ∠CVG=∠HBM, ∠VGC=∠BMH, △VGC is similar to △BMH.. Find the value of x.
问题：如图所示，BM=16，GC=x，MH=22，VG=12，∠CVG=∠HBM，∠VGC=∠BMH，三角形VGC相似于三角形BMH。求x的值。
Construction (CDL):
Shape(VG,GC,CV)
Shape(BM,MH,HB)
Conditions (CDL):
Equal(LengthOfLine(BM),16)
Equal(LengthOfLine(GC),x)
Equal(LengthOfLine(MH),22)
Equal(LengthOfLine(VG),12)
Equal(MeasureOfAngle(CVG),MeasureOfAngle(HBM))
Equal(MeasureOfAngle(VGC),MeasureOfAngle(BMH))
SimilarBetweenTriangle(VGC,BMH)
Goal: Value(x)
Answer: 33/2
Theorem sequence:
similar_triangle_property_line_ratio(1,VGC,BMH)
similar_triangle_property_line_ratio(1,CVG,HBM)
Problem: As shown in the diagram, AB=x, AC=x-4, BC=8, BC⊥AC. Find the value of x.
问题：如图所示，AB=x，AC=x-4，BC=8，BC⊥AC。求x的值。
Construction (CDL):
Shape(AB,BC,CA)
Conditions (CDL):
Equal(LengthOfLine(AB),x)
Equal(LengthOfLine(AC),x-4)
Equal(LengthOfLine(BC),8)
PerpendicularBetweenLine(BC,AC)
Goal: Value(x)
Answer: 10
Theorem sequence:
right_triangle_judgment_angle(1,BCA)
right_triangle_property_pythagorean(1,BCA)
Problem: As shown in the diagram, ∠EDF=2*x°, ∠FAC=139°, ∠GBD=9*x°, ∠HCB=6*x°. Find the value of x.
问题：如图所示，∠EDF=2*x°，∠FAC=139°，∠GBD=9*x°，∠HCB=6*x°。求x的值。
Construction (CDL):
Shape(FA,AC)
Shape(HC,CB)
Shape(GB,BD)
Shape(ED,DA)
Shape(AD,DB,BC,CA)
Collinear(FAD)
Collinear(ACH)
Collinear(EDB)
Collinear(GBC)
Conditions (CDL):
Equal(MeasureOfAngle(EDF),2*x)
Equal(MeasureOfAngle(FAC),139)
Equal(MeasureOfAngle(GBD),9*x)
Equal(MeasureOfAngle(HCB),6*x)
Goal: Value(x)
Answer: 13
Theorem sequence:
adjacent_complementary_angle(1,EDA,ADB)
adjacent_complementary_angle(1,FAC,CAD)
adjacent_complementary_angle(1,HCB,BCA)
adjacent_complementary_angle(1,GBD,DBC)
quadrilateral_property_angle_sum(1,ADBC)
Problem: As shown in the diagram, NO=6, OP=10, PN=x, the center of ⊙O is O, PN is the tangent to circle O. Find the value of x.
问题：如图所示，NO=6，OP=10，PN=x，O是圆O的圆心，PN是圆O的切线。求x的值。
Construction (CDL):
Shape(AO,ON,ONA)
Shape(NO,OA,OAN)
Shape(AP,PN,OAN)
Collinear(OAP)
Cocircular(O,NA)
Conditions (CDL):
Equal(LengthOfLine(NO),6)
Equal(LengthOfLine(OP),10)
Equal(LengthOfLine(PN),x)
IsCentreOfCircle(O,O)
IsTangentOfCircle(PN,O)
Goal: Value(x)
Answer: 8
Theorem sequence:
tangent_of_circle_property_perpendicular(2,PN,O,O)
right_triangle_judgment_angle(1,PNO)
right_triangle_property_pythagorean(1,PNO)
Problem: As shown in the diagram, ∠JKL=x+10°, ∠KLM=x°, ∠LMJ=2*x-8°, ∠MJK=3*x-6°. Find the measure of ∠MJK.
问题：如图所示，∠JKL=x+10°，∠KLM=x°，∠LMJ=2*x-8°，∠MJK=3*x-6°。求∠MJK的大小。
Construction (CDL):
Shape(JK,KL,LM,MJ)
Conditions (CDL):
Equal(MeasureOfAngle(JKL),x+10)
Equal(MeasureOfAngle(KLM),x)
Equal(MeasureOfAngle(LMJ),2*x-8)
Equal(MeasureOfAngle(MJK),3*x-6)
Goal: Value(MeasureOfAngle(MJK))
Answer: 150
Theorem sequence:
quadrilateral_property_angle_sum(1,JKLM)
Problem: As shown in the diagram, AB=13, AC=12, BC=5, ∠BAC=x°, AC⊥BC. Find tan(x).
问题：如图所示，AB=13，AC=12，BC=5，∠BAC=x°，AC⊥BC。求tan(x)。
Construction (CDL):
Shape(AC,CB,BA)
Conditions (CDL):
Equal(LengthOfLine(AB),13)
Equal(LengthOfLine(AC),12)
Equal(LengthOfLine(BC),5)
Equal(MeasureOfAngle(BAC),x)
PerpendicularBetweenLine(AC,BC)
Goal: Value(Tan(x))
Answer: 5/12
Theorem sequence:
sine_theorem(1,ACB)
sine_theorem(1,CBA)
Problem: As shown in the diagram, JK=6*x-5, LK=4*x+3, MP=3*y+8, QP=5*y-7, QP=MP, MJ is parallel to PK, PK is parallel to QL. Find the value of x.
问题：如图所示，JK=6*x-5，LK=4*x+3，MP=3*y+8，QP=5*y-7，QP=MP，MJ∥PK，PK∥QL。求x的值。
Construction (CDL):
Shape(GJ,JA)
Shape(AJ,JK)
Shape(JK,KB)
Shape(BK,KL)
Shape(KL,LC)
Shape(CL,LY)
Shape(MJ,JG)
Shape(HM,MJ)
Shape(JM,MP,PK,KJ)
Shape(KP,PQ,QL,LK)
Shape(YL,LQ)
Shape(LQ,QZ)
Shape(DM,MH)
Shape(PM,MD)
Shape(EP,PM)
Shape(QP,PE)
Shape(FQ,QP)
Shape(ZQ,QF)
Collinear(GJKLY)
Collinear(HMPQZ)
Collinear(AJMD)
Collinear(BKPE)
Collinear(CLQF)
Conditions (CDL):
Equal(LengthOfLine(JK),6*x-5)
Equal(LengthOfLine(LK),4*x+3)
Equal(LengthOfLine(MP),3*y+8)
Equal(LengthOfLine(QP),5*y-7)
Equal(LengthOfLine(QP),LengthOfLine(MP))
ParallelBetweenLine(MJ,PK)
ParallelBetweenLine(PK,QL)
Goal: Value(x)
Answer: 4
Theorem sequence:
parallel_judgment_par_par(1,MJ,PK,QL)
trapezoid_judgment_parallel(1,MQLJ)
midsegment_of_quadrilateral_judgment_parallel(1,PK,MQLJ)
Problem: As shown in the diagram, ∠ADB=11*x-1°, ∠BDF=7*y-4°, ∠DFH=7*x+9°, ∠GAD=2*y+5°, ∠HFC=z°, AG is parallel to DB, DB is parallel to FH. Find the value of y.
问题：如图所示，∠ADB=11*x-1°，∠BDF=7*y-4°，∠DFH=7*x+9°，∠GAD=2*y+5°，∠HFC=z°，AG平行于DB，DB平行于FH。求y的值。
Construction (CDL):
Shape(HF,FC)
Shape(BD,DF)
Shape(DF,FH)
Shape(AD,DB)
Shape(GA,AD)
Shape(EA,AG)
Shape(FD,DA)
Collinear(CFD)
Collinear(EAD)
Conditions (CDL):
Equal(MeasureOfAngle(ADB),11*x-1)
Equal(MeasureOfAngle(BDF),7*y-4)
Equal(MeasureOfAngle(DFH),7*x+9)
Equal(MeasureOfAngle(GAD),2*y+5)
Equal(MeasureOfAngle(HFC),z)
ParallelBetweenLine(AG,DB)
ParallelBetweenLine(DB,FH)
Goal: Value(y)
Answer: 11
Theorem sequence:
parallel_property_ipsilateral_internal_angle(1,AG,DB)
parallel_property_ipsilateral_internal_angle(1,DB,FH)
Problem: As shown in the diagram, JL=5*x-6, KJ=3*x+6, KJ=LK, KL=4*x, LK=JL. Find the length of line KL.
问题：如图所示，JL=5*x-6，KJ=3*x+6，KJ=LK，KL=4*x，LK=JL。求直线KL的长度。
Construction (CDL):
Shape(KJ,JL,LK)
Conditions (CDL):
Equal(LengthOfLine(JL),5*x-6)
Equal(LengthOfLine(KJ),3*x+6)
Equal(LengthOfLine(KJ),LengthOfLine(LK))
Equal(LengthOfLine(KL),4*x)
Equal(LengthOfLine(LK),LengthOfLine(JL))
Goal: Value(LengthOfLine(KL))
Answer: 24
Theorem sequence:
Problem: As shown in the diagram, ∠CDF=52°, ∠DHG=38°, HG is perpendicular to DG. Find the measure of ∠GDH.
问题：如图所示，∠CDF=52°，∠DHG=38°，HG⊥DG。求∠GDH的大小。
Construction (CDL):
Shape(BH,HI)
Shape(IH,HD)
Shape(HD,DC)
Shape(CD,DF)
Shape(FD,DG)
Shape(DG,GA)
Shape(AG,GE)
Shape(EG,GH)
Shape(GH,HB)
Shape(HG,GD,DH)
Collinear(IHGA)
Collinear(EGDC)
Collinear(BHDF)
Conditions (CDL):
Equal(MeasureOfAngle(CDF),52)
Equal(MeasureOfAngle(DHG),38)
PerpendicularBetweenLine(HG,DG)
Goal: Value(MeasureOfAngle(GDH))
Answer: 52
Theorem sequence:
triangle_property_angle_sum(1,HGD)
Problem: As shown in the diagram, XY=2, the radius of ⊙W is 4, the radius of circle Z is 7, W is the center of ⊙W, Z is the center of ⊙Z, CX is the diameter of ⊙Z. Find the length of line IC.
问题：如图所示，XY=2，圆W的半径为4，⊙Z的半径为7，W是圆W的圆心，Z是圆Z的圆心，CX是圆Z的直径。求直线IC的长度。
Construction (CDL):
Shape(IW,WX,ZAX,WAI)
Shape(XI,WIB,ZXB)
Shape(WYA,ZAX,XY)
Shape(YX,ZXB,WBY)
Shape(YZ,ZC,ZCA,WYA)
Shape(CZ,ZY,WBY,ZBC)
Collinear(IWXYZC)
Cocircular(W,IBYA)
Cocircular(Z,XBCA)
Conditions (CDL):
Equal(LengthOfLine(XY),2)
Equal(RadiusOfCircle(W),4)
Equal(RadiusOfCircle(Z),7)
IsCentreOfCircle(W,W)
IsCentreOfCircle(Z,Z)
IsDiameterOfCircle(CX,Z)
Goal: Value(LengthOfLine(IC))
Answer: 20
Theorem sequence:
radius_of_circle_property_length_equal(1,WI,W)
radius_of_circle_property_length_equal(1,WY,W)
diameter_of_circle_property_length_equal(1,CX,Z)
circle_property_length_of_radius_and_diameter(1,Z)
line_addition(1,WX,XY)
line_addition(1,IW,WX)
line_addition(1,IX,XC)
Problem: As shown in the diagram, AE=3, AF=x, DE=9, the tangent to circle B is AF. Find the value of x.
问题：如图所示，AE=3，AF=x，DE=9，AF是⊙O的切线。求x的值。
Construction (CDL):
Shape(DB,BE,BEF,BFD)
Shape(BEF,EA,AF)
Shape(EB,BD,BDE)
Collinear(DBEA)
Cocircular(B,DEF)
Conditions (CDL):
Equal(LengthOfLine(AE),3)
Equal(LengthOfLine(AF),x)
Equal(LengthOfLine(DE),9)
IsTangentOfCircle(AF,B)
Goal: Value(x)
Answer: 6
Theorem sequence:
line_addition(1,AE,ED)
circle_property_circular_power_tangent_and_segment_line(1,AF,AED,B)
Problem: As shown in the diagram, RV=x, WT=15, ZY=8, YZ is the midsegment of quadrilateral TVRW. Find the value of x.
问题：如图所示，RV=x，WT=15，ZY=8，TVRW的中位线为YZ。求x的值。
Construction (CDL):
Shape(TY,YZ,ZW,WT)
Shape(YV,VR,RZ,ZY)
Collinear(TYV)
Collinear(WZR)
Conditions (CDL):
Equal(LengthOfLine(RV),x)
Equal(LengthOfLine(WT),15)
Equal(LengthOfLine(ZY),8)
IsMidsegmentOfQuadrilateral(YZ,TVRW)
Goal: Value(x)
Answer: 1
Theorem sequence:
midsegment_of_quadrilateral_property_length(1,YZ,TVRW)
Problem: As shown in the diagram, PQ=QS, QR=RS, ∠SRP=72°. Find the measure of ∠QPS.
问题：如图所示，PQ=QS，QR=RS，∠SRP=72°。求∠QPS的大小。
Construction (CDL):
Shape(SR,RQ,QS)
Shape(SQ,QP,PS)
Collinear(RQP)
Conditions (CDL):
Equal(LengthOfLine(PQ),LengthOfLine(QS))
Equal(LengthOfLine(QR),LengthOfLine(RS))
Equal(MeasureOfAngle(SRP),72)
Goal: Value(MeasureOfAngle(QPS))
Answer: 27
Theorem sequence:
triangle_property_angle_sum(1,SRQ)
triangle_property_angle_sum(1,SQP)
isosceles_triangle_judgment_line_equal(1,RQS)
isosceles_triangle_property_angle_equal(1,RQS)
isosceles_triangle_judgment_line_equal(1,QPS)
isosceles_triangle_property_angle_equal(1,QPS)
adjacent_complementary_angle(1,RQS,SQP)
Problem: As shown in the diagram, BA=5*x, BC=3*y-4, DA=29, DC=25, ∠ADF=34°, ∠DCF=54°, ∠FAD=49°, BADC is a parallelogram. Find the value of y.
问题：如图所示，BA=5*x，BC=3*y-4，DA=29，DC=25，∠ADF=34°，∠DCF=54°，∠FAD=49°，BADC是平行四边形。求y的值。
Construction (CDL):
Shape(BA,AF,FB)
Shape(FA,AD,DF)
Shape(FD,DC,CF)
Shape(FC,CB,BF)
Collinear(BFD)
Collinear(AFC)
Conditions (CDL):
Equal(LengthOfLine(BA),5*x)
Equal(LengthOfLine(BC),3*y-4)
Equal(LengthOfLine(DA),29)
Equal(LengthOfLine(DC),25)
Equal(MeasureOfAngle(ADF),34)
Equal(MeasureOfAngle(DCF),54)
Equal(MeasureOfAngle(FAD),49)
Parallelogram(BADC)
Goal: Value(y)
Answer: 11
Theorem sequence:
parallelogram_property_opposite_line_equal(1,ADCB)
Problem: As shown in the diagram, CE=5, the center of circle E is E. Find the diameter of ⊙E.
问题：如图所示，CE=5，圆E的圆心为E。求圆E的直径。
Construction (CDL):
Shape(AE,EB,BA)
Shape(AB,EBA)
Shape(DE,EA,EAD)
Shape(CE,ED,EDC)
Shape(BE,EC,ECB)
Collinear(AEC)
Collinear(DEB)
Cocircular(E,ADCB)
Conditions (CDL):
Equal(LengthOfLine(CE),5)
IsCentreOfCircle(E,E)
Goal: Value(DiameterOfCircle(E))
Answer: 10
Theorem sequence:
radius_of_circle_property_length_equal(1,EC,E)
circle_property_length_of_radius_and_diameter(1,E)
Problem: As shown in the diagram, AB=2, CB=3, ∠EBA=25°, AE⊥BE. Find the area of △ACB.
问题：如图所示，AB=2，CB=3，∠EBA=25°，AE⊥BE。求△ACB的面积。
Construction (CDL):
Shape(AC,CE,EA)
Shape(AE,EB,BA)
Collinear(CEB)
Conditions (CDL):
Equal(LengthOfLine(AB),2)
Equal(LengthOfLine(CB),3)
Equal(MeasureOfAngle(EBA),25)
PerpendicularBetweenLine(AE,BE)
Goal: Value(AreaOfTriangle(ACB))
Answer: 3*sin(5*pi/36)
Theorem sequence:
triangle_area_formula_sine(1,BAC)
Problem: As shown in the diagram, ∠BAE=58°, ∠CBE=26°, ∠EBA=47°, AB is parallel to EC. Find the measure of ∠DCE.
问题：如图所示，∠BAE=58°，∠CBE=26°，∠EBA=47°，AB平行于EC。求∠DCE的大小。
Construction (CDL):
Shape(AE,EB,BA)
Shape(BE,EC,CB)
Shape(CE,ED,DC)
Collinear(AED)
Collinear(BCD)
Conditions (CDL):
Equal(MeasureOfAngle(BAE),58)
Equal(MeasureOfAngle(CBE),26)
Equal(MeasureOfAngle(EBA),47)
ParallelBetweenLine(AB,EC)
Goal: Value(MeasureOfAngle(DCE))
Answer: 73
Theorem sequence:
angle_addition(1,CBE,EBA)
parallel_property_corresponding_angle(1,CE,BA,D)
Problem: As shown in the diagram, AF=EA, CF=DC, FT=12, QD=EQ. Find the length of line TQ.
问题：如图所示，AF=EA，CF=DC，FT=12，QD=EQ。求直线TQ的长度。
Construction (CDL):
Shape(FA,AT,TF)
Shape(AE,ET,TA)
Shape(TE,EQ,QT)
Shape(TQ,QD,DT)
Shape(TD,DC,CT)
Shape(TC,CF,FT)
Collinear(EAF)
Collinear(FTQ)
Collinear(ETC)
Collinear(FCD)
Collinear(EQD)
Collinear(ATD)
Conditions (CDL):
Equal(LengthOfLine(AF),LengthOfLine(EA))
Equal(LengthOfLine(CF),LengthOfLine(DC))
Equal(LengthOfLine(FT),12)
Equal(LengthOfLine(QD),LengthOfLine(EQ))
Goal: Value(LengthOfLine(TQ))
Answer: 6
Theorem sequence:
median_of_triangle_judgment(1,DA,DFE)
median_of_triangle_judgment(1,FQ,FED)
centroid_of_triangle_judgment_intersection(1,T,EDF,Q,A)
centroid_of_triangle_property_line_ratio(1,T,FED,Q)
Problem: As shown in the diagram, JK=2*b+3, JM=3*a, LK=21, LM=45, ∠MLR=30°, ∠RLK=70°, JMLK is a parallelogram. Find the measure of ∠LKJ.
问题：如图所示，JK=2*b+3，JM=3*a，LK=21，LM=45，∠MLR=30°，∠RLK=70°，JMLK是平行四边形。求∠LKJ的大小。
Construction (CDL):
Shape(MR,RJ,JM)
Shape(RM,ML,LR)
Shape(RL,LK,KR)
Shape(RK,KJ,JR)
Collinear(JRL)
Collinear(MRK)
Conditions (CDL):
Equal(LengthOfLine(JK),2*b+3)
Equal(LengthOfLine(JM),3*a)
Equal(LengthOfLine(LK),21)
Equal(LengthOfLine(LM),45)
Equal(MeasureOfAngle(MLR),30)
Equal(MeasureOfAngle(RLK),70)
Parallelogram(JMLK)
Goal: Value(MeasureOfAngle(LKJ))
Answer: 80
Theorem sequence:
angle_addition(1,MLR,RLK)
parallel_property_ipsilateral_internal_angle(1,LM,KJ)
Problem: As shown in the diagram, AD=5, BD=6, AB is perpendicular to CB, CD⊥BD. Find the length of line BC.
问题：如图所示，AD=5，BD=6，AB⊥CB，CD垂直于BD。求直线BC的长度。
Construction (CDL):
Shape(AB,BD,DA)
Shape(DB,BC,CD)
Collinear(ADC)
Conditions (CDL):
Equal(LengthOfLine(AD),5)
Equal(LengthOfLine(BD),6)
PerpendicularBetweenLine(AB,CB)
PerpendicularBetweenLine(CD,BD)
Goal: Value(LengthOfLine(BC))
Answer: 6*sqrt(61)/5
Theorem sequence:
adjacent_complementary_angle(1,CDB,BDA)
line_addition(1,AD,DC)
mirror_similar_triangle_judgment_aa(1,BDA,CAB)
right_triangle_judgment_angle(1,CDB)
right_triangle_property_pythagorean(1,CDB)
mirror_similar_triangle_property_line_ratio(1,BDA,CAB)
mirror_similar_triangle_property_line_ratio(1,DAB,BCA)
mirror_similar_triangle_property_line_ratio(1,ABD,ABC)
Problem: As shown in the diagram, AB=10, AC=x, BC=6, CB⊥AB. Find the value of x.
问题：如图所示，AB=10，AC=x，BC=6，CB⊥AB。求x的值。
Construction (CDL):
Shape(AC,CB,BA)
Conditions (CDL):
Equal(LengthOfLine(AB),10)
Equal(LengthOfLine(AC),x)
Equal(LengthOfLine(BC),6)
PerpendicularBetweenLine(CB,AB)
Goal: Value(x)
Answer: 2*sqrt(34)
Theorem sequence:
right_triangle_judgment_angle(1,CBA)
right_triangle_property_pythagorean(1,CBA)
Problem: As shown in the diagram, AY=9, XA=5, XZ is perpendicular to YZ, ZA⊥XA. Find the length of line ZA.
问题：如图所示，AY=9，XA=5，XZ⊥YZ，ZA垂直于XA。求直线ZA的长度。
Construction (CDL):
Shape(XZ,ZA,AX)
Shape(AZ,ZY,YA)
Collinear(XAY)
Conditions (CDL):
Equal(LengthOfLine(AY),9)
Equal(LengthOfLine(XA),5)
PerpendicularBetweenLine(XZ,YZ)
PerpendicularBetweenLine(ZA,XA)
Goal: Value(LengthOfLine(ZA))
Answer: 3*sqrt(5)
Theorem sequence:
line_addition(1,XA,AY)
adjacent_complementary_angle(1,YAZ,ZAX)
mirror_similar_triangle_judgment_aa(1,ZAX,YXZ)
mirror_similar_triangle_judgment_aa(1,ZYA,XZY)
mirror_similar_triangle_property_line_ratio(1,ZAX,YXZ)
mirror_similar_triangle_property_line_ratio(1,AXZ,ZYX)
mirror_similar_triangle_property_line_ratio(1,XZA,XZY)
mirror_similar_triangle_property_line_ratio(1,ZYA,XZY)
mirror_similar_triangle_property_line_ratio(1,YAZ,YXZ)
Problem: As shown in the diagram, LM=6, ∠LKJ=109°, MJ and LK are opposite sides of the parallelogram JMLK. Find the length of line JK.
问题：如图所示，LM=6，∠LKJ=109°，MJ和LK是▱JMLK的一组对边。求直线JK的长度。
Construction (CDL):
Shape(JM,ML,LK,KJ)
Conditions (CDL):
Equal(LengthOfLine(LM),6)
Equal(MeasureOfAngle(LKJ),109)
Parallelogram(JMLK)
Goal: Value(LengthOfLine(JK))
Answer: 6
Theorem sequence:
parallelogram_property_opposite_line_equal(1,MLKJ)
Problem: As shown in the diagram, ∠WXV=14°, the center of circle F is F. Find the measure of ⌒FXV.
问题：如图所示，∠WXV=14°，F是圆F的圆心。求弧FXV的角度。
Construction (CDL):
Shape(OWX,XF,FW)
Shape(OXV,VX)
Shape(FX,XV,VF)
Shape(WF,FV,FVW)
Collinear(WFX)
Cocircular(F,WXV)
Conditions (CDL):
Equal(MeasureOfAngle(WXV),14)
IsCentreOfCircle(F,F)
Goal: Value(MeasureOfArc(FXV))
Answer: 152
Theorem sequence:
arc_property_center_angle(1,FXV,F)
radius_of_circle_property_length_equal(1,FV,F)
radius_of_circle_property_length_equal(1,FX,F)
isosceles_triangle_judgment_line_equal(1,FXV)
isosceles_triangle_property_angle_equal(1,FXV)
triangle_property_angle_sum(1,FXV)
Problem: As shown in the diagram, the area of quadrilateral BCDA is 100, AB=x+15, BE=x, BCDA is a ▱, CE⊥BE. Find the height of BCDA.
问题：如图所示，BCDA的面积为100，AB=x+15，BE=x，BCDA是平行四边形，CE⊥BE。求BCDA的高。
Construction (CDL):
Shape(CE,EB,BC)
Shape(ED,DA,AB,BE)
Collinear(CED)
Conditions (CDL):
Equal(AreaOfQuadrilateral(BCDA),100)
Equal(LengthOfLine(AB),x+15)
Equal(LengthOfLine(BE),x)
Parallelogram(BCDA)
PerpendicularBetweenLine(CE,BE)
Goal: Value(HeightOfQuadrilateral(BCDA))
Answer: 5
Theorem sequence:
altitude_of_quadrilateral_judgment_left_vertex(1,BE,BCDA)
parallelogram_property_opposite_line_equal(1,CDAB)
parallelogram_area_formula_common(1,BCDA)
Problem: As shown in the diagram, ∠CGH=42°, ∠DGC=3*x°, ∠GCD=z°, ∠GHC=y°, ∠HCG=48°, GD is parallel to HC, HG∥CD. Find the value of z.
问题：如图所示，∠CGH=42°，∠DGC=3*x°，∠GCD=z°，∠GHC=y°，∠HCG=48°，GD∥HC，HG∥CD。求z的值。
Construction (CDL):
Shape(GH,HC,CG)
Shape(CD,DG,GC)
Conditions (CDL):
Equal(MeasureOfAngle(CGH),42)
Equal(MeasureOfAngle(DGC),3*x)
Equal(MeasureOfAngle(GCD),z)
Equal(MeasureOfAngle(GHC),y)
Equal(MeasureOfAngle(HCG),48)
ParallelBetweenLine(GD,HC)
ParallelBetweenLine(HG,CD)
Goal: Value(z)
Answer: 42
Theorem sequence:
parallelogram_judgment_parallel_and_parallel(1,GHCD)
parallel_property_alternate_interior_angle(1,GD,HC)
angle_addition(1,DGC,CGH)
angle_addition(1,HCG,GCD)
parallelogram_property_opposite_angle_equal(1,GHCD)
Problem: As shown in the diagram, AC=BC, CD=AD, ∠ADC=92°. Find the measure of ∠ACB.
问题：如图所示，AC=BC，CD=AD，∠ADC=92°。求∠ACB的大小。
Construction (CDL):
Shape(AD,DC,CA)
Shape(AC,CB,BA)
Collinear(DCB)
Conditions (CDL):
Equal(LengthOfLine(AC),LengthOfLine(BC))
Equal(LengthOfLine(CD),LengthOfLine(AD))
Equal(MeasureOfAngle(ADC),92)
Goal: Value(MeasureOfAngle(ACB))
Answer: 136
Theorem sequence:
isosceles_triangle_judgment_line_equal(1,DCA)
isosceles_triangle_property_angle_equal(1,DCA)
angle_addition(1,BAC,CAD)
triangle_property_angle_sum(1,ADC)
triangle_property_angle_sum(1,ACB)
triangle_property_angle_sum(1,DBA)
Problem: As shown in the diagram, ∠ACE=109°, ∠DAE=24°, ∠EBD=95°, ∠EDA=33°. Find the measure of ∠AED.
问题：如图所示，∠ACE=109°，∠DAE=24°，∠EBD=95°，∠EDA=33°。求∠AED的大小。
Construction (CDL):
Shape(BD,DE,EB)
Shape(ED,DA,AE)
Shape(EA,AC,CE)
Collinear(BEA)
Collinear(DEC)
Conditions (CDL):
Equal(MeasureOfAngle(ACE),109)
Equal(MeasureOfAngle(DAE),24)
Equal(MeasureOfAngle(EBD),95)
Equal(MeasureOfAngle(EDA),33)
Goal: Value(MeasureOfAngle(AED))
Answer: 123
Theorem sequence:
triangle_property_angle_sum(1,EDA)
Problem: As shown in the diagram, ∠EBC=3°, the measure of ⌒HCE is 5*x-6, the measure of arc HJC is 4*x+8. Find the value of x.
问题：如图所示，∠EBC=3°，弧HCE的角度为5*x-6，⌒HJC的角度为4*x+8。求x的值。
Construction (CDL):
Shape(BC,HJC,JB)
Shape(HJC,HCE,EJ)
Shape(JE,HEJ)
Collinear(EJB)
Cocircular(H,CEJ)
Conditions (CDL):
Equal(MeasureOfAngle(EBC),3)
Equal(MeasureOfArc(HCE),5*x-6)
Equal(MeasureOfArc(HJC),4*x+8)
Goal: Value(x)
Answer: 20
Theorem sequence:
circle_property_circular_power_tangent_and_segment_angle(2,BC,BJE,H)
Problem: As shown in the diagram, AR=RC, AT=16, CM=7, CT=TB, RM=4, SA=SB. Find the length of line CS.
问题：如图所示，AR=RC，AT=16，CM=7，CT=TB，RM=4，SA=SB。求直线CS的长度。
Construction (CDL):
Shape(AR,RM,MA)
Shape(MR,RC,CM)
Shape(MC,CT,TM)
Shape(MT,TB,BM)
Shape(MB,BS,SM)
Shape(MS,SA,AM)
Collinear(ARC)
Collinear(CTB)
Collinear(ASB)
Collinear(CMS)
Collinear(AMT)
Collinear(RMB)
Conditions (CDL):
Equal(LengthOfLine(AR),LengthOfLine(RC))
Equal(LengthOfLine(AT),16)
Equal(LengthOfLine(CM),7)
Equal(LengthOfLine(CT),LengthOfLine(TB))
Equal(LengthOfLine(RM),4)
Equal(LengthOfLine(SA),LengthOfLine(SB))
Goal: Value(LengthOfLine(CS))
Answer: 21/2
Theorem sequence:
median_of_triangle_judgment(1,BR,BAC)
median_of_triangle_judgment(1,AT,ACB)
centroid_of_triangle_judgment_intersection(1,M,CBA,T,R)
centroid_of_triangle_property_line_ratio(1,M,CBA,S)
line_addition(1,CM,MS)
Problem: As shown in the diagram, ∠WVU=34°, the measure of arc BCX is 128, the measure of ⌒BWU is x. Find the value of x.
问题：如图所示，∠WVU=34°，弧BCX的角度为128，⌒BWU的角度为x。求x的值。
Construction (CDL):
Shape(WV,VU,BWU)
Shape(WX,BXW)
Shape(CU,BUC)
Shape(BWU,UC,BCX,XW)
Collinear(VWX)
Collinear(VUC)
Cocircular(B,WUCX)
Conditions (CDL):
Equal(MeasureOfAngle(WVU),34)
Equal(MeasureOfArc(BCX),128)
Equal(MeasureOfArc(BWU),x)
Goal: Value(x)
Answer: 60
Theorem sequence:
circle_property_circular_power_segment_and_segment_angle(1,VWX,VUC,B)