SunnyLin/FormalGeo7k_v1 huggingface dataset:
Problem: As shown in the diagram, AB=5, BC=3, O bisects segment AC. Find the length of line OB.
问题：如图所示，AB=5，BC=3，O是线段AC的中点。求直线OB的长度。
Construction (CDL):
Collinear(AOBC)
Conditions (CDL):
Equal(LengthOfLine(AB),5)
Equal(LengthOfLine(BC),3)
IsMidpointOfLine(O,AC)
Goal: Value(LengthOfLine(OB))
Answer: 1
Theorem sequence:
line_addition(1,AO,OB)
line_addition(1,AB,BC)
line_addition(1,AO,OC)
Problem: As shown in the diagram, ∠ACD=32°, ∠BAC=70°, ∠DBA=40°. Find the measure of ∠BDC.
问题：如图所示，∠ACD=32°，∠BAC=70°，∠DBA=40°。求∠BDC的大小。
Construction (CDL):
Shape(AC,CD,DB,BA)
Shape(BD,DC)
Conditions (CDL):
Equal(MeasureOfAngle(ACD),32)
Equal(MeasureOfAngle(BAC),70)
Equal(MeasureOfAngle(DBA),40)
Goal: Value(MeasureOfAngle(BDC))
Answer: 142
Theorem sequence:
quadrilateral_property_angle_sum(1,ACDB)
round_angle(1,BDC,CDB)
Problem: As shown in the diagram, ∠AOC=56°, ∠COD=90°, ∠DOB=73°. Find the measure of ∠BOA.
问题：如图所示，∠AOC=56°，∠COD=90°，∠DOB=73°。求∠BOA的大小。
Construction (CDL):
Shape(AO,OC)
Shape(CO,OD)
Shape(DO,OB)
Shape(BO,OA)
Conditions (CDL):
Equal(MeasureOfAngle(AOC),56)
Equal(MeasureOfAngle(COD),90)
Equal(MeasureOfAngle(DOB),73)
Goal: Value(MeasureOfAngle(BOA))
Answer: 141
Theorem sequence:
angle_addition(1,AOC,COD)
angle_addition(1,AOD,DOB)
round_angle(1,AOB,BOA)
Problem: As shown in the diagram, AB=10, BD=4, C bisects segment AD. Find the length of line BC.
问题：如图所示，AB=10，BD=4，C平分线段AD。求直线BC的长度。
Construction (CDL):
Collinear(ACDB)
Conditions (CDL):
Equal(LengthOfLine(AB),10)
Equal(LengthOfLine(BD),4)
IsMidpointOfLine(C,AD)
Goal: Value(LengthOfLine(BC))
Answer: 7
Theorem sequence:
line_addition(1,AD,DB)
line_addition(1,AC,CD)
line_addition(1,CD,DB)
Problem: As shown in the diagram, ∠CBE=15°, ∠DAB=30°, BE is parallel to DA. Find the measure of ∠CBA.
问题：如图所示，∠CBE=15°，∠DAB=30°，BE平行于DA。求∠CBA的大小。
Construction (CDL):
Shape(DA,AB)
Shape(EB,BA)
Shape(CB,BE)
Conditions (CDL):
Equal(MeasureOfAngle(CBE),15)
Equal(MeasureOfAngle(DAB),30)
ParallelBetweenLine(BE,DA)
Goal: Value(MeasureOfAngle(CBA))
Answer: 45
Theorem sequence:
parallel_property_alternate_interior_angle(1,BE,DA)
angle_addition(1,CBE,EBA)
Problem: As shown in the diagram, AC=Mul(3/4,LengthOfLine(CB)), CB=60. Find the length of line AB.
问题：如图所示，AC=Mul(3/4,LengthOfLine(CB))，CB=60。求直线AB的长度。
Construction (CDL):
Collinear(ACB)
Conditions (CDL):
Equal(LengthOfLine(AC),Mul(3/4,LengthOfLine(CB)))
Equal(LengthOfLine(CB),60)
Goal: Value(LengthOfLine(AB))
Answer: 105
Theorem sequence:
line_addition(1,AC,CB)
Problem: As shown in the diagram, AB=10, CD is the median of triangle CAB. Find the length of line AD.
问题：如图所示，AB=10，CD是△CAB的中线。求直线AD的长度。
Construction (CDL):
Shape(CA,AD,DC)
Shape(CD,DB,BC)
Collinear(ADB)
Conditions (CDL):
Equal(LengthOfLine(AB),10)
IsMedianOfTriangle(CD,CAB)
Goal: Value(LengthOfLine(AD))
Answer: 5
Theorem sequence:
line_addition(1,AD,DB)
Problem: As shown in the diagram, ∠COB=Sub(Mul(3,MeasureOfAngle(AOC)),20)°. Find the measure of ∠AOC.
问题：如图所示，∠COB=Sub(Mul(3,MeasureOfAngle(AOC)),20)°。求∠AOC的大小。
Construction (CDL):
Shape(AO,OC)
Shape(CO,OB)
Collinear(AOB)
Conditions (CDL):
Equal(MeasureOfAngle(COB),Sub(Mul(3,MeasureOfAngle(AOC)),20))
Goal: Value(MeasureOfAngle(AOC))
Answer: 50
Theorem sequence:
adjacent_complementary_angle(1,AOC,COB)
Problem: As shown in the diagram, ∠DAB=75°, ∠EBC=25°, DABC is a ▱. Find the measure of ∠CEB.
问题：如图所示，∠DAB=75°，∠EBC=25°，AD和BC是▱DABC的一组对边。求∠CEB的大小。
Construction (CDL):
Shape(ED,DA,AB,BE)
Shape(CE,EB,BC)
Collinear(DEC)
Conditions (CDL):
Equal(MeasureOfAngle(DAB),75)
Equal(MeasureOfAngle(EBC),25)
Parallelogram(DABC)
Goal: Value(MeasureOfAngle(CEB))
Answer: 80
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
triangle_property_angle_sum(1,CEB)
Problem: As shown in the diagram, ∠ABC=50°, ∠ACD=140°. Find the measure of ∠CAB.
问题：如图所示，∠ABC=50°，∠ACD=140°。求∠CAB的大小。
Construction (CDL):
Shape(AB,BC,CA)
Shape(AC,CD)
Collinear(BCD)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),50)
Equal(MeasureOfAngle(ACD),140)
Goal: Value(MeasureOfAngle(CAB))
Answer: 90
Theorem sequence:
triangle_property_angle_sum(1,ABC)
adjacent_complementary_angle(1,BCA,ACD)
Problem: As shown in the diagram, ∠COB=140°. Find the measure of ∠AOC.
问题：如图所示，∠COB=140°。求∠AOC的大小。
Construction (CDL):
Shape(AO,OC)
Shape(CO,OB)
Collinear(AOB)
Conditions (CDL):
Equal(MeasureOfAngle(COB),140)
Goal: Value(MeasureOfAngle(AOC))
Answer: 40
Theorem sequence:
adjacent_complementary_angle(1,AOC,COB)
Problem: As shown in the diagram, CB=Mul(3,LengthOfLine(AC)), CD=2, D bisects segment AB. Find the length of line AB.
问题：如图所示，CB=Mul(3,LengthOfLine(AC))，CD=2，D是线段AB的中点。求直线AB的长度。
Construction (CDL):
Collinear(ACDB)
Conditions (CDL):
Equal(LengthOfLine(CB),Mul(3,LengthOfLine(AC)))
Equal(LengthOfLine(CD),2)
IsMidpointOfLine(D,AB)
Goal: Value(LengthOfLine(AB))
Answer: 8
Theorem sequence:
line_addition(1,AC,CD)
line_addition(1,AC,CB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, CB=Mul(2,LengthOfLine(AC)), DC=2, D bisects segment AB. Find the length of line AB.
问题：如图所示，CB=Mul(2,LengthOfLine(AC))，DC=2，D是线段AB的中点。求直线AB的长度。
Construction (CDL):
Collinear(ACDB)
Conditions (CDL):
Equal(LengthOfLine(CB),Mul(2,LengthOfLine(AC)))
Equal(LengthOfLine(DC),2)
IsMidpointOfLine(D,AB)
Goal: Value(LengthOfLine(AB))
Answer: 12
Theorem sequence:
line_addition(1,AC,CD)
line_addition(1,AC,CB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AC=4, BC=6, M is the midpoint of segment AC, N bisects segment CB. Find the length of line MN.
问题：如图所示，AC=4，BC=6，M平分线段AC，N是线段CB的中点。求直线MN的长度。
Construction (CDL):
Collinear(AMCNB)
Conditions (CDL):
Equal(LengthOfLine(AC),4)
Equal(LengthOfLine(BC),6)
IsMidpointOfLine(M,AC)
IsMidpointOfLine(N,CB)
Goal: Value(LengthOfLine(MN))
Answer: 5
Theorem sequence:
line_addition(1,AM,MC)
line_addition(1,AM,MN)
line_addition(1,AC,CN)
line_addition(1,AC,CB)
line_addition(1,AN,NB)
Problem: As shown in the diagram, AB=10, BC=3, D is the midpoint of segment AC, E bisects segment AB. Find the length of line DE.
问题：如图所示，AB=10，BC=3，D是线段AC的中点，E是线段AB的中点。求直线DE的长度。
Construction (CDL):
Collinear(ADECB)
Conditions (CDL):
Equal(LengthOfLine(AB),10)
Equal(LengthOfLine(BC),3)
IsMidpointOfLine(D,AC)
IsMidpointOfLine(E,AB)
Goal: Value(LengthOfLine(DE))
Answer: 3/2
Theorem sequence:
line_addition(1,AD,DE)
line_addition(1,AD,DC)
line_addition(1,AE,EB)
line_addition(1,AC,CB)
Problem: As shown in the diagram, AB=10, NM=1, C bisects segment MB, M bisects segment AB. Find the length of line NC.
问题：如图所示，AB=10，NM=1，C平分线段MB，M是线段AB的中点。求直线NC的长度。
Construction (CDL):
Collinear(ANMCB)
Conditions (CDL):
Equal(LengthOfLine(AB),10)
Equal(LengthOfLine(NM),1)
IsMidpointOfLine(C,MB)
IsMidpointOfLine(M,AB)
Goal: Value(LengthOfLine(NC))
Answer: 7/2
Theorem sequence:
line_addition(1,AN,NM)
line_addition(1,AN,NC)
line_addition(1,AM,MC)
line_addition(1,AM,MB)
line_addition(1,AC,CB)
Problem: As shown in the diagram, ∠AQF=100°, ∠BPA=126°. Find the measure of ∠DAP minus the measure of ∠QFD.
问题：如图所示，∠AQF=100°，∠BPA=126°。求∠DAP的大小减去∠QFD的大小。
Construction (CDL):
Shape(AB,BP,PA)
Shape(PB,BC,CP)
Shape(AP,PD,DA)
Shape(PC,CQ,QD,DP)
Shape(AD,DF,FA)
Shape(DQ,QF,FD)
Collinear(BPDF)
Collinear(APC)
Collinear(ADQ)
Collinear(BCQ)
Conditions (CDL):
Equal(MeasureOfAngle(AQF),100)
Equal(MeasureOfAngle(BPA),126)
Goal: Value(Sub(MeasureOfAngle(DAP),MeasureOfAngle(QFD)))
Answer: 46
Theorem sequence:
adjacent_complementary_angle(1,BPA,APD)
triangle_property_angle_sum(1,APD)
triangle_property_angle_sum(1,DQF)
vertical_angle(1,PDA,FDQ)
Problem: As shown in the diagram, ∠BCA=70°, BD is the altitude of triangle BCA, CE is the angle bisector of ∠BCA. Find the measure of ∠BOE.
问题：如图所示，∠BCA=70°，BD是△BCA的高，CE平分∠BCA。求∠BOE的大小。
Construction (CDL):
Shape(AE,EO,OD,DA)
Shape(EB,BO,OE)
Shape(OB,BC,CO)
Shape(DO,OC,CD)
Collinear(AEB)
Collinear(ADC)
Collinear(EOC)
Collinear(BOD)
Conditions (CDL):
Equal(MeasureOfAngle(BCA),70)
IsAltitudeOfTriangle(BD,BCA)
IsBisectorOfAngle(CE,BCA)
Goal: Value(MeasureOfAngle(BOE))
Answer: 55
Theorem sequence:
angle_addition(1,BCE,ECA)
triangle_property_angle_sum(1,DOC)
vertical_angle(1,BOE,DOC)
Problem: As shown in the diagram, AB=7, BC=3, D bisects segment AC. Find the length of line DB.
问题：如图所示，AB=7，BC=3，D是线段AC的中点。求直线DB的长度。
Construction (CDL):
Collinear(ADBC)
Conditions (CDL):
Equal(LengthOfLine(AB),7)
Equal(LengthOfLine(BC),3)
IsMidpointOfLine(D,AC)
Goal: Value(LengthOfLine(DB))
Answer: 2
Theorem sequence:
line_addition(1,AD,DB)
line_addition(1,AD,DC)
line_addition(1,AB,BC)
Problem: As shown in the diagram, ∠CAB=45°, ∠EDF=30°, ∠BCA is the right angle of the right triangle BCA, ∠FED is the right angle of the right △ FED. Find the sum of the measure of ∠ARD and the measure of ∠ESB.
问题：如图所示，∠CAB=45°，∠EDF=30°，BC和CA是直角△BCA的两个直角边，FE和ED是直角△FED的两个直角边。求∠ARD的大小与∠ESB的大小之和。
Construction (CDL):
Shape(DO,OC)
Shape(CP,PE)
Shape(ES,SB)
Shape(BH,HF)
Shape(FQ,QA)
Shape(AR,RD)
Shape(CO,OP,PC)
Shape(EP,PS,SE)
Shape(BS,SH,HB)
Shape(FH,HQ,QF)
Shape(RA,AQ,QR)
Shape(DR,RO,OD)
Shape(OR,RQ,QH,HS,SP,PO)
Collinear(DOPE)
Collinear(ESHF)
Collinear(FQRD)
Collinear(CORA)
Collinear(CPSB)
Collinear(AQHB)
Conditions (CDL):
Equal(MeasureOfAngle(CAB),45)
Equal(MeasureOfAngle(EDF),30)
RightTriangle(BCA)
RightTriangle(FED)
Goal: Value(Add(MeasureOfAngle(ARD),MeasureOfAngle(ESB)))
Answer: 210
Theorem sequence:
adjacent_complementary_angle(1,ARD,DRO)
adjacent_complementary_angle(1,PSE,ESB)
triangle_property_angle_sum(1,COP)
triangle_property_angle_sum(1,DRO)
triangle_property_angle_sum(1,SEP)
vertical_angle(1,ROD,COP)
vertical_angle(1,OPC,EPS)
Problem: As shown in the diagram, ∠CAB=20°, AB is parallel to DE, EC⊥AC. Find the measure of ∠CEF.
问题：如图所示，∠CAB=20°，AB∥DE，EC垂直于AC。求∠CEF的大小。
Construction (CDL):
Shape(CA,AB,BC)
Shape(AD,DE,EB,BA)
Shape(BE,EF)
Collinear(CBE)
Collinear(DEF)
Conditions (CDL):
Equal(MeasureOfAngle(CAB),20)
ParallelBetweenLine(AB,DE)
PerpendicularBetweenLine(EC,AC)
Goal: Value(MeasureOfAngle(CEF))
Answer: 110
Theorem sequence:
triangle_property_angle_sum(1,CAB)
parallel_property_corresponding_angle(2,ED,BA,C)
adjacent_complementary_angle(1,DEC,CEF)
Problem: As shown in the diagram, ∠ABC=60°, ∠CAB=80°. Find the measure of ∠ACD.
问题：如图所示，∠ABC=60°，∠CAB=80°。求∠ACD的大小。
Construction (CDL):
Shape(AB,BC,CA)
Shape(AC,CD)
Collinear(BCD)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),60)
Equal(MeasureOfAngle(CAB),80)
Goal: Value(MeasureOfAngle(ACD))
Answer: 140
Theorem sequence:
triangle_property_angle_sum(1,ABC)
adjacent_complementary_angle(1,BCA,ACD)
Problem: As shown in the diagram, Add(MeasureOfAngle(BCD)=MeasureOfAngle(CDA)), AC is the angle bisector of ∠DAB, BP bisects ∠CBE. Find the measure of ∠BPC.
问题：如图所示，Add(MeasureOfAngle(BCD)=MeasureOfAngle(CDA))，AC平分∠DAB，BP是∠CBE的角平分线。求∠BPC的大小。
Construction (CDL):
Shape(DA,AC,CD)
Shape(PD,DC,CP)
Shape(CA,AB,BC)
Shape(PC,CB,BP)
Shape(PB,BE,EP)
Collinear(ACP)
Collinear(ABE)
Conditions (CDL):
Equal(Add(MeasureOfAngle(BCD),MeasureOfAngle(CDA)),200)
IsBisectorOfAngle(AC,DAB)
IsBisectorOfAngle(BP,CBE)
Goal: Value(MeasureOfAngle(BPC))
Answer: 10
Theorem sequence:
quadrilateral_property_angle_sum(1,DABC)
angle_addition(1,DAC,CAB)
angle_addition(1,CBP,PBE)
angle_addition(1,ABC,CBP)
adjacent_complementary_angle(1,ABC,CBE)
triangle_property_angle_sum(1,PAB)
Problem: As shown in the diagram, ∠BAC=45°, ∠EFD=35°, △BAC is mirror similar to △EFD.. Find the measure of ∠DEF.
问题：如图所示，∠BAC=45°，∠EFD=35°，三角形BAC与三角形EFD是镜像相似三角形。求∠DEF的大小。
Construction (CDL):
Shape(BA,AC,CB)
Shape(DE,EF,FD)
Conditions (CDL):
Equal(MeasureOfAngle(BAC),45)
Equal(MeasureOfAngle(EFD),35)
MirrorSimilarBetweenTriangle(BAC,EFD)
Goal: Value(MeasureOfAngle(DEF))
Answer: 100
Theorem sequence:
mirror_similar_triangle_property_angle_equal(1,ACB,DEF)
triangle_property_angle_sum(1,DEF)
Problem: As shown in the diagram, ∠ABP=20°, ∠ACP=50°, BP is the angle bisector of ∠ABC, CP is the angle bisector of ∠ACM. Find the measure of ∠CAB.
问题：如图所示，∠ABP=20°，∠ACP=50°，BP是∠ABC的角平分线，CP平分∠ACM。求∠CAB的大小。
Construction (CDL):
Shape(AB,BO,OA)
Shape(OB,BC,CO)
Shape(AO,OP,PA)
Shape(PO,OC,CP)
Shape(PC,CM,MP)
Collinear(AOC)
Collinear(BOP)
Collinear(BCM)
Conditions (CDL):
Equal(MeasureOfAngle(ABP),20)
Equal(MeasureOfAngle(ACP),50)
IsBisectorOfAngle(BP,ABC)
IsBisectorOfAngle(CP,ACM)
Goal: Value(MeasureOfAngle(CAB))
Answer: 60
Theorem sequence:
angle_addition(1,ABP,PBC)
angle_addition(1,ACP,PCM)
adjacent_complementary_angle(1,BCA,ACM)
triangle_property_angle_sum(1,ABC)
Problem: As shown in the diagram, ∠CDB=125°, NA is perpendicular to QA. Find the sum of the measure of ∠CDB, the measure of ∠EAB, the measure of ∠NME, the measure of ∠ENM, the measure of ∠BPQ and the measure of ∠PQB.
问题：如图所示，∠CDB=125°，NA垂直于QA。求∠CDB的大小、∠EAB的大小、∠NME的大小、∠ENM的大小、∠BPQ的大小与∠PQB的大小之和。
Construction (CDL):
Shape(ME,EN,NM)
Shape(MA,AE,EM)
Shape(AP,PB,BA)
Shape(BP,PQ,QB)
Shape(BQ,QC,CD,DB)
Shape(NE,ED,DC,CN)
Shape(AB,BD,DE,EA)
Collinear(MEDC)
Collinear(AEN)
Collinear(ABQ)
Collinear(PBD)
Conditions (CDL):
Equal(MeasureOfAngle(CDB),125)
PerpendicularBetweenLine(NA,QA)
Goal: Value(Add(MeasureOfAngle(CDB),MeasureOfAngle(EAB),MeasureOfAngle(NME),MeasureOfAngle(ENM),MeasureOfAngle(BPQ),MeasureOfAngle(PQB)))
Answer: 360
Theorem sequence:
adjacent_complementary_angle(1,CDB,BDE)
quadrilateral_property_angle_sum(1,ABDE)
vertical_angle(1,MEN,DEA)
vertical_angle(1,ABD,QBP)
triangle_property_angle_sum(1,MEN)
triangle_property_angle_sum(1,PQB)
Problem: As shown in the diagram, ∠ABC=30°, ∠CAB=110°. Find the measure of ∠BCA.
问题：如图所示，∠ABC=30°，∠CAB=110°。求∠BCA的大小。
Construction (CDL):
Shape(CA,AB,BC)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),30)
Equal(MeasureOfAngle(CAB),110)
Goal: Value(MeasureOfAngle(BCA))
Answer: 40
Theorem sequence:
triangle_property_angle_sum(1,BCA)
Problem: As shown in the diagram, ∠CEB=60°, ∠CPA=70°, AP bisects ∠EAD, CP bisects ∠ECD. Find the measure of ∠CDQ.
问题：如图所示，∠CEB=60°，∠CPA=70°，AP平分∠EAD，CP平分∠ECD。求∠CDQ的大小。
Construction (CDL):
Shape(EA,AO,OE)
Shape(OA,AF,FO)
Shape(PO,OF,FQ,QP)
Shape(AB,BC,CF,FA)
Shape(FC,CQ,QF)
Shape(QC,CD,DQ)
Collinear(EAB)
Collinear(EOFC)
Collinear(POA)
Collinear(PQC)
Collinear(AFQD)
Conditions (CDL):
Equal(MeasureOfAngle(CEB),60)
Equal(MeasureOfAngle(CPA),70)
IsBisectorOfAngle(AP,EAD)
IsBisectorOfAngle(CP,ECD)
Goal: Value(MeasureOfAngle(CDQ))
Answer: 80
Theorem sequence:
triangle_property_angle_sum(1,EAO)
triangle_property_angle_sum(1,PAQ)
triangle_property_angle_sum(1,POC)
triangle_property_angle_sum(1,QCD)
vertical_angle(1,AOE,POC)
vertical_angle(1,AQP,DQC)
Problem: As shown in the diagram, AF=AE, GF=GE, ∠DCA=140°, CD∥AB. Find the measure of ∠AHC.
问题：如图所示，AF=AE，GF=GE，∠DCA=140°，CD∥AB。求∠AHC的大小。
Construction (CDL):
Shape(CF,FG,GH,HC)
Shape(FA,AG,GF)
Shape(GA,AE,EG)
Shape(HG,GE,EB,BD,DH)
Collinear(AFC)
Collinear(AEB)
Collinear(AGH)
Collinear(CHD)
Conditions (CDL):
Equal(LengthOfLine(AF),LengthOfLine(AE))
Equal(LengthOfLine(GF),LengthOfLine(GE))
Equal(MeasureOfAngle(DCA),140)
ParallelBetweenLine(CD,AB)
Goal: Value(MeasureOfAngle(AHC))
Answer: 20
Theorem sequence:
mirror_congruent_triangle_judgment_sss(1,AEG,AGF)
mirror_congruent_triangle_property_angle_equal(1,AEG,AGF)
parallel_property_collinear_extend(3,CD,AB,H)
parallel_property_alternate_interior_angle(2,CH,AB)
triangle_property_angle_sum(1,CAH)
Problem: As shown in the diagram, ∠CAB=110°. Find the sum of the measure of ∠EDB and the measure of ∠CED.
问题：如图所示，∠CAB=110°。求∠EDB的大小与∠CED的大小之和。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(MeasureOfAngle(CAB),110)
Goal: Value(Add(MeasureOfAngle(EDB),MeasureOfAngle(CED)))
Answer: 290
Theorem sequence:
adjacent_complementary_angle(1,ADE,EDB)
adjacent_complementary_angle(1,CED,DEA)
triangle_property_angle_sum(1,ADE)
Problem: As shown in the diagram, Add(MeasureOfAngle(FDB)=MeasureOfAngle(CEG)), DE bisects ∠ADF, ED bisects ∠GEA. Find the measure of ∠CAB.
问题：如图所示，Add(MeasureOfAngle(FDB)=MeasureOfAngle(CEG))，DE是∠ADF的角平分线，ED平分∠GEA。求∠CAB的大小。
Construction (CDL):
Shape(BF,FD,DB)
Shape(DF,FG,GE,ED)
Shape(EG,GC,CE)
Shape(AD,DE,EA)
Collinear(BDA)
Collinear(BFGC)
Collinear(CEA)
Conditions (CDL):
Equal(Add(MeasureOfAngle(FDB),MeasureOfAngle(CEG)),60)
IsBisectorOfAngle(DE,ADF)
IsBisectorOfAngle(ED,GEA)
Goal: Value(MeasureOfAngle(CAB))
Answer: 30
Theorem sequence:
angle_addition(1,ADE,EDF)
angle_addition(1,GED,DEA)
adjacent_complementary_angle(1,ADF,FDB)
adjacent_complementary_angle(1,CEG,GEA)
triangle_property_angle_sum(1,ADE)
Problem: As shown in the diagram, ∠CAB=80°. Find the sum of the measure of ∠EDB and the measure of ∠CED.
问题：如图所示，∠CAB=80°。求∠EDB的大小与∠CED的大小之和。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(MeasureOfAngle(CAB),80)
Goal: Value(Add(MeasureOfAngle(EDB),MeasureOfAngle(CED)))
Answer: 260
Theorem sequence:
adjacent_complementary_angle(1,ADE,EDB)
adjacent_complementary_angle(1,CED,DEA)
triangle_property_angle_sum(1,ADE)
Problem: As shown in the diagram, AB=5, BC=3, the perimeter of △ABD is 11, BD is the median of triangle BCA. Find the perimeter of triangle BCD.
问题：如图所示，AB=5，BC=3，△ABD的周长为11，BD是三角形BCA的中线。求三角形BCD的周长。
Construction (CDL):
Shape(AB,BD,DA)
Shape(DB,BC,CD)
Collinear(ADC)
Conditions (CDL):
Equal(LengthOfLine(AB),5)
Equal(LengthOfLine(BC),3)
Equal(PerimeterOfTriangle(ABD),11)
IsMedianOfTriangle(BD,BCA)
Goal: Value(PerimeterOfTriangle(BCD))
Answer: 9
Theorem sequence:
triangle_perimeter_formula(1,ABD)
triangle_perimeter_formula(1,DBC)
Problem: As shown in the diagram, ∠COB=60°. Find the measure of ∠AOC.
问题：如图所示，∠COB=60°。求∠AOC的大小。
Construction (CDL):
Shape(AO,OC)
Shape(CO,OB)
Collinear(AOB)
Conditions (CDL):
Equal(MeasureOfAngle(COB),60)
Goal: Value(MeasureOfAngle(AOC))
Answer: 120
Theorem sequence:
adjacent_complementary_angle(1,AOC,COB)
Problem: As shown in the diagram, CB=3, DB=5, D bisects segment AC. Find the length of line AB.
问题：如图所示，CB=3，DB=5，D是线段AC的中点。求直线AB的长度。
Construction (CDL):
Collinear(ADCB)
Conditions (CDL):
Equal(LengthOfLine(CB),3)
Equal(LengthOfLine(DB),5)
IsMidpointOfLine(D,AC)
Goal: Value(LengthOfLine(AB))
Answer: 7
Theorem sequence:
line_addition(1,AD,DB)
line_addition(1,DC,CB)
Problem: As shown in the diagram, ∠ABO=∠CBD, ∠CDE=45°, ∠COB=130°, ∠OCA=∠DCB, FA⊥BA. Find the measure of ∠FAC.
问题：如图所示，∠ABO=∠CBD，∠CDE=45°，∠COB=130°，∠OCA=∠DCB，FA⊥BA。求∠FAC的大小。
Construction (CDL):
Shape(AB,BO,OC,CA)
Shape(OB,BC,CO)
Shape(AC,CF,FA)
Shape(BD,DC,CB)
Shape(CD,DE,EF,FC)
Collinear(BCF)
Collinear(BDE)
Conditions (CDL):
Equal(MeasureOfAngle(ABO),MeasureOfAngle(CBD))
Equal(MeasureOfAngle(CDE),45)
Equal(MeasureOfAngle(COB),130)
Equal(MeasureOfAngle(OCA),MeasureOfAngle(DCB))
PerpendicularBetweenLine(FA,BA)
Goal: Value(MeasureOfAngle(FAC))
Answer: 5
Theorem sequence:
adjacent_complementary_angle(1,BDC,CDE)
round_angle(1,COB,BOC)
triangle_property_angle_sum(1,CBD)
quadrilateral_property_angle_sum(1,ABOC)
angle_addition(1,FAC,CAB)
Problem: As shown in the diagram, ∠CBE=45°, ∠EBA=60°. Find the measure of ∠CBA.
问题：如图所示，∠CBE=45°，∠EBA=60°。求∠CBA的大小。
Construction (CDL):
Shape(AE,EB,BA)
Shape(EC,CB,BE)
Collinear(AEC)
Conditions (CDL):
Equal(MeasureOfAngle(CBE),45)
Equal(MeasureOfAngle(EBA),60)
Goal: Value(MeasureOfAngle(CBA))
Answer: 105
Theorem sequence:
angle_addition(1,CBE,EBA)
Problem: As shown in the diagram, BE=EC, DE=2, EC=4. Find the length of line BD.
问题：如图所示，BE=EC，DE=2，EC=4。求直线BD的长度。
Construction (CDL):
Shape(AB,BD,DA)
Shape(AD,DE,EA)
Shape(AE,EC,CA)
Collinear(BDEC)
Conditions (CDL):
Equal(LengthOfLine(BE),LengthOfLine(EC))
Equal(LengthOfLine(DE),2)
Equal(LengthOfLine(EC),4)
Goal: Value(LengthOfLine(BD))
Answer: 2
Theorem sequence:
line_addition(1,BD,DE)
Problem: As shown in the diagram, ∠CBP=∠PBA, ∠CDP=∠PDA, ∠DAB=40°, ∠DPB=38°. Find the measure of ∠DCB.
问题：如图所示，∠CBP=∠PBA，∠CDP=∠PDA，∠DAB=40°，∠DPB=38°。求∠DCB的大小。
Construction (CDL):
Shape(AE,ED,DA)
Shape(DE,EG,GD)
Shape(EP,PF,FG,GE)
Shape(GF,FB,BG)
Shape(FC,CB,BF)
Collinear(AEGB)
Collinear(PFB)
Collinear(DEP)
Collinear(DGFC)
Conditions (CDL):
Equal(MeasureOfAngle(CBP),MeasureOfAngle(PBA))
Equal(MeasureOfAngle(CDP),MeasureOfAngle(PDA))
Equal(MeasureOfAngle(DAB),40)
Equal(MeasureOfAngle(DPB),38)
Goal: Value(MeasureOfAngle(DCB))
Answer: 36
Theorem sequence:
triangle_property_angle_sum(1,AED)
triangle_property_angle_sum(1,PBE)
triangle_property_angle_sum(1,FCB)
triangle_property_angle_sum(1,PFD)
vertical_angle(1,AED,BEP)
vertical_angle(1,PFD,BFC)
Problem: As shown in the diagram, AB=16, AC=CD, AD=DB. Find the length of line CD.
问题：如图所示，AB=16，AC=CD，AD=DB。求直线CD的长度。
Construction (CDL):
Shape(AC)
Shape(CD)
Shape(DB)
Collinear(ACDB)
Conditions (CDL):
Equal(LengthOfLine(AB),16)
Equal(LengthOfLine(AC),LengthOfLine(CD))
Equal(LengthOfLine(AD),LengthOfLine(DB))
Goal: Value(LengthOfLine(CD))
Answer: 4
Theorem sequence:
line_addition(1,AC,CD)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AB=18, BC=6, CD=DB. Find the length of line AD.
问题：如图所示，AB=18，BC=6，CD=DB。求直线AD的长度。
Construction (CDL):
Shape(AC)
Shape(CD)
Shape(DB)
Collinear(ACDB)
Conditions (CDL):
Equal(LengthOfLine(AB),18)
Equal(LengthOfLine(BC),6)
Equal(LengthOfLine(CD),LengthOfLine(DB))
Goal: Value(LengthOfLine(AD))
Answer: 15
Theorem sequence:
line_addition(1,AC,CD)
line_addition(1,AC,CB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AB=14, AD=DC, DC=4. Find the length of line CB.
问题：如图所示，AB=14，AD=DC，DC=4。求直线CB的长度。
Construction (CDL):
Shape(AD)
Shape(DC)
Shape(CB)
Collinear(ADCB)
Conditions (CDL):
Equal(LengthOfLine(AB),14)
Equal(LengthOfLine(AD),LengthOfLine(DC))
Equal(LengthOfLine(DC),4)
Goal: Value(LengthOfLine(CB))
Answer: 6
Theorem sequence:
line_addition(1,AD,DB)
line_addition(1,DC,CB)
Problem: As shown in the diagram, AB=8, AM=MB, BC=4, BN=NC. Find the length of line MN.
问题：如图所示，AB=8，AM=MB，BC=4，BN=NC。求直线MN的长度。
Construction (CDL):
Shape(AM)
Shape(MB)
Shape(BN)
Shape(NC)
Collinear(AMBNC)
Conditions (CDL):
Equal(LengthOfLine(AB),8)
Equal(LengthOfLine(AM),LengthOfLine(MB))
Equal(LengthOfLine(BC),4)
Equal(LengthOfLine(BN),LengthOfLine(NC))
Goal: Value(LengthOfLine(MN))
Answer: 6
Theorem sequence:
line_addition(1,AM,MB)
line_addition(1,AM,MN)
line_addition(1,AB,BN)
line_addition(1,AB,BC)
line_addition(1,AN,NC)
Problem: As shown in the diagram, AB=10, AC=6, CD=DB. Find the length of line AD.
问题：如图所示，AB=10，AC=6，CD=DB。求直线AD的长度。
Construction (CDL):
Shape(AC)
Shape(CD)
Shape(DB)
Collinear(ACDB)
Conditions (CDL):
Equal(LengthOfLine(AB),10)
Equal(LengthOfLine(AC),6)
Equal(LengthOfLine(CD),LengthOfLine(DB))
Goal: Value(LengthOfLine(AD))
Answer: 8
Theorem sequence:
line_addition(1,AC,CD)
line_addition(1,AD,DB)
Problem: As shown in the diagram, ∠BCD=110°, O is the center of ⊙O. Find the measure of ∠DOB.
问题：如图所示，∠BCD=110°，O是⊙O的圆心。求∠DOB的大小。
Construction (CDL):
Shape(BA,OAB)
Shape(CB,OBC)
Shape(DC,OCD)
Shape(AD,ODA)
Shape(AB,BO,OD,DA)
Shape(OB,BC,CD,DO)
Cocircular(O,ABCD)
Conditions (CDL):
Equal(MeasureOfAngle(BCD),110)
IsCentreOfCircle(O,O)
Goal: Value(MeasureOfAngle(DOB))
Answer: 140
Theorem sequence:
arc_property_center_angle(1,OBD,O)
arc_property_circumference_angle_internal(1,OBD,C)
Problem: As shown in the diagram, ∠ADC=110°, O is the center of circle O. Find the measure of ∠COA.
问题：如图所示，∠ADC=110°，O是⊙O的圆心。求∠COA的大小。
Construction (CDL):
Shape(AB,OBA)
Shape(BC,OCB)
Shape(DA,OAD)
Shape(CD,ODC)
Shape(BA,AO,OC,CB)
Shape(OA,AD,DC,CO)
Cocircular(O,ADCB)
Conditions (CDL):
Equal(MeasureOfAngle(ADC),110)
IsCentreOfCircle(O,O)
Goal: Value(MeasureOfAngle(COA))
Answer: 140
Theorem sequence:
arc_property_circumference_angle_internal(1,OAC,D)
arc_property_center_angle(1,OAC,O)
Problem: As shown in the diagram, ∠DOB=110°, the center of circle O is O. Find the measure of ∠BCD.
问题：如图所示，∠DOB=110°，⊙O的圆心为O。求∠BCD的大小。
Construction (CDL):
Shape(AD,ODA)
Shape(BA,OAB)
Shape(CB,OBC)
Shape(DC,OCD)
Shape(DA,AB,BO,OD)
Shape(DO,OB,BC,CD)
Cocircular(O,ABCD)
Conditions (CDL):
Equal(MeasureOfAngle(DOB),110)
IsCentreOfCircle(O,O)
Goal: Value(MeasureOfAngle(BCD))
Answer: 125
Theorem sequence:
arc_property_center_angle(1,OBD,O)
arc_property_circumference_angle_internal(1,OBD,C)
Problem: As shown in the diagram, ∠AEC=68°, ∠DAB=40°. Find the measure of ∠ADC.
问题：如图所示，∠AEC=68°，∠DAB=40°。求∠ADC的大小。
Construction (CDL):
Shape(BA,OAB)
Shape(DE,EB,OBD)
Shape(CD,ODC)
Shape(AE,EC,OCA)
Shape(BE,EA,AB)
Shape(ED,DC,CE)
Collinear(BEC)
Collinear(AED)
Cocircular(O,BDCA)
Conditions (CDL):
Equal(MeasureOfAngle(AEC),68)
Equal(MeasureOfAngle(DAB),40)
Goal: Value(MeasureOfAngle(ADC))
Answer: 28
Theorem sequence:
adjacent_complementary_angle(1,BEA,AEC)
triangle_property_angle_sum(1,BEA)
arc_property_circumference_angle_external(1,OCA,B)
arc_property_circumference_angle_external(1,OCA,D)