images images listlengths 1 1 | problem stringlengths 310 675 | answer stringlengths 75 1.18k | proID stringlengths 1 4 |
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<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, DG=3, AE is the angle bisector of ∠DAB, F is the midpoint of segment CD, AD and BC are opposite sides of the ▱ ABCD, DG⊥FG. Find the length of line AE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide ... | consCDL:['Shape(AG,GD,DA)', 'Shape(DG,GF,FD)', 'Shape(FC,CE,EF)', 'Shape(AB,BC,CF,FG,GA)', 'Collinear(AGFE)', 'Collinear(DFC)', 'Collinear(BCE)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(DG),3)', 'PerpendicularBetweenLine(DG,FG)'], textCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(DG),3)', 'I... | 6406 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4, CE=3, AE is the angle bisector of ∠DAB, AD and BC are opposite sides of the ▱ ABCD. Find the perimeter of quadrilateral ABCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its ca... | consCDL:['Shape(AB,BE,EA)', 'Shape(AE,EC,CD,DA)', 'Collinear(BEC)'], imgCDL:['Equal(LengthOfLine(AB),4)', 'Equal(LengthOfLine(CE),3)'], textCDL:['Equal(LengthOfLine(AB),4)', 'Equal(LengthOfLine(CE),3)', 'IsBisectorOfAngle(AE,DAB)', 'Parallelogram(ABCD)']. | 6409 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the height of ABCD is 2, BC=3, ABCD is a parallelogram. Find the area of quadrilateral ABCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></... | consCDL:['Shape(AB,BC,CD,DA)'], imgCDL:['Equal(LengthOfLine(BC),3)'], textCDL:['Equal(HeightOfQuadrilateral(ABCD),2)', 'Equal(LengthOfLine(BC),3)', 'Parallelogram(ABCD)']. | 6412 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=6, AD=9, ∠DAB=120°, AE bisects ∠DAB, quadrilateral ABCD is a ▱. Find the perimeter of △EFC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think>... | consCDL:['Shape(AB,BE,EA)', 'Shape(AE,EC,CD,DA)', 'Shape(EF,FC,CE)', 'Collinear(BEC)', 'Collinear(DCF)', 'Collinear(AEF)'], imgCDL:['Equal(LengthOfLine(AB),6)', 'Equal(LengthOfLine(AD),9)', 'Equal(MeasureOfAngle(DAB),120)'], textCDL:['Equal(LengthOfLine(AB),6)', 'Equal(LengthOfLine(AD),9)', 'Equal(MeasureOfAngle(DAB),1... | 6420 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4, BC=6, OE=2, ABCD is a parallelogram. Find the perimeter of EFCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then p... | consCDL:['Shape(AB,BO,OA)', 'Shape(OB,BF,FO)', 'Shape(OF,FC,CO)', 'Shape(OC,CD,DO)', 'Shape(OD,DE,EO)', 'Shape(OE,EA,AO)', 'Collinear(AOC)', 'Collinear(BOD)', 'Collinear(EOF)', 'Collinear(AED)', 'Collinear(BFC)'], imgCDL:['Equal(LengthOfLine(AB),4)', 'Equal(LengthOfLine(BC),6)', 'Equal(LengthOfLine(OE),2)'], textCDL:['... | 6432 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=60°, ABCD is a parallelogram. Find the measure of ∠CDA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all... | consCDL:['Shape(AB,BC,CD,DA)'], imgCDL:['Equal(MeasureOfAngle(ABC),60)'], textCDL:['Equal(MeasureOfAngle(ABC),60)', 'Parallelogram(ABCD)']. | 6435 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=3, BE=2, AE is the angle bisector of ∠DAB, BE is the angle bisector of ∠ABC, quadrilateral ABCD is a parallelogram. Find Area(△ABE). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on it... | consCDL:['Shape(DA,AE,ED)', 'Shape(EA,AB,BE)', 'Shape(EB,BC,CE)', 'Collinear(DEC)'], imgCDL:['Equal(LengthOfLine(AE),3)', 'Equal(LengthOfLine(BE),2)'], textCDL:['Equal(LengthOfLine(AE),3)', 'Equal(LengthOfLine(BE),2)', 'IsBisectorOfAngle(AE,DAB)', 'IsBisectorOfAngle(BE,ABC)', 'Parallelogram(ABCD)']. | 6443 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BD=12, the perimeter of quadrilateral ABCD is 36, E bisects segment CD, quadrilateral ABCD is a ▱. Find Perimeter(△DOE). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You ... | consCDL:['Shape(AB,BO,OA)', 'Shape(OB,BC,CO)', 'Shape(OC,CE,EO)', 'Shape(OE,ED,DO)', 'Shape(OD,DA,AO)', 'Collinear(AOC)', 'Collinear(BOD)', 'Collinear(CED)'], imgCDL:['Equal(LengthOfLine(BD),12)'], textCDL:['Equal(LengthOfLine(BD),12)', 'Equal(PerimeterOfQuadrilateral(ABCD),36)', 'IsMidpointOfLine(E,CD)', 'Parallelogra... | 6446 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=4, BC=7, CE bisects ∠BCD, AD and BC are opposite sides of the ▱ ABCD. Find the length of line AB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <... | consCDL:['Shape(AB,BC,CE,EA)', 'Shape(EC,CD,DE)', 'Collinear(AED)'], imgCDL:['Equal(LengthOfLine(AE),4)', 'Equal(LengthOfLine(BC),7)'], textCDL:['Equal(LengthOfLine(AE),4)', 'Equal(LengthOfLine(BC),7)', 'IsBisectorOfAngle(CE,BCD)', 'Parallelogram(ABCD)']. | 6448 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, DE=2, DF=3, E is the midpoint of segment CD, ABCD is a ▱. Find the perimeter of ABCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> ... | consCDL:['Shape(FD,DE,EF)', 'Shape(DA,AB,BE,ED)', 'Shape(EB,BC,CE)', 'Collinear(FEB)', 'Collinear(DEC)', 'Collinear(FDA)'], imgCDL:['Equal(LengthOfLine(DE),2)', 'Equal(LengthOfLine(DF),3)'], textCDL:['Equal(LengthOfLine(DE),2)', 'Equal(LengthOfLine(DF),3)', 'IsMidpointOfLine(E,CD)', 'Parallelogram(ABCD)']. | 6457 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AM=MD, AM=MF, ∠MAF=70°, quadrilateral ABCD is a ▱, AM and BN are opposite sides of the parallelogram MABN, MFEN is a parallelogram. Find ∠FMA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL base... | consCDL:['Shape(DM,MN,NC,CD)', 'Shape(MF,FB,BN,NM)', 'Shape(MA,AF,FM)', 'Shape(NB,BE,EN)', 'Collinear(DMA)', 'Collinear(CNB)', 'Collinear(AFBE)'], imgCDL:['Equal(LengthOfLine(AM),LengthOfLine(MD))', 'Equal(LengthOfLine(AM),LengthOfLine(MF))', 'Equal(MeasureOfAngle(MAF),70)'], textCDL:['Equal(LengthOfLine(AM),LengthOfLi... | 6462 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, AD=6, OF=3, ABCD is a parallelogram. Find Perimeter(BCEF). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provid... | consCDL:['Shape(OA,AF,FO)', 'Shape(OF,FB,BO)', 'Shape(OB,BC,CO)', 'Shape(OC,CE,EO)', 'Shape(OE,ED,DO)', 'Shape(OD,DA,AO)', 'Collinear(DEC)', 'Collinear(AFB)', 'Collinear(EOF)', 'Collinear(DOB)', 'Collinear(AOC)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AD),6)', 'Equal(LengthOfLine(OF),3)'], textCDL:[... | 6471 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAE=125°, ABCD is a ▱, CE is perpendicular to BE. Find the measure of ∠BCE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and ... | consCDL:['Shape(AE,EC,CD,DA)', 'Shape(EB,BC,CE)', 'Collinear(AEB)'], imgCDL:['Equal(MeasureOfAngle(DAE),125)', 'PerpendicularBetweenLine(CE,BE)'], textCDL:['Equal(MeasureOfAngle(DAE),125)', 'Parallelogram(ABCD)', 'PerpendicularBetweenLine(CE,BE)']. | 6490 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the sum of the length of line AC and BD is 18, BC=6, ABCD is a ▱. Find the perimeter of triangle AOD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within ... | consCDL:['Shape(AB,BO,OA)', 'Shape(AO,OD,DA)', 'Shape(OB,BC,CO)', 'Shape(OC,CD,DO)', 'Collinear(AOC)', 'Collinear(BOD)'], imgCDL:['Equal(LengthOfLine(BC),6)'], textCDL:['Equal(Add(LengthOfLine(AC),LengthOfLine(BD)),18)', 'Equal(LengthOfLine(BC),6)', 'Parallelogram(ABCD)']. | 6492 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=8, E is the midpoint of segment AD, ABCD is a parallelogram. Find the length of line OE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></t... | consCDL:['Shape(DE,EO,OD)', 'Shape(EA,AO,OE)', 'Shape(DO,OC,CD)', 'Shape(OA,AB,BO)', 'Shape(OB,BC,CO)', 'Collinear(DOB)', 'Collinear(AOC)', 'Collinear(AED)'], imgCDL:['Equal(LengthOfLine(AB),8)'], textCDL:['Equal(LengthOfLine(AB),8)', 'IsMidpointOfLine(E,AD)', 'Parallelogram(ABCD)']. | 6495 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, Perimeter(ABCD) is 16, quadrilateral ABCD is a ▱, AO⊥EO. Find Perimeter(△DEC). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags an... | consCDL:['Shape(AO,OE,EA)', 'Shape(EO,OF,FE)', 'Shape(EF,FD,DE)', 'Shape(FO,OC,CF)', 'Shape(FC,CD,DF)', 'Shape(AB,BO,OA)', 'Shape(OB,BC,CO)', 'Collinear(AOC)', 'Collinear(BOFD)', 'Collinear(AED)', 'Collinear(EFC)'], imgCDL:['PerpendicularBetweenLine(AO,EO)'], textCDL:['Equal(PerimeterOfQuadrilateral(ABCD),16)', 'Parall... | 6497 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4, AD=3, OF=3/2, quadrilateral ABCD is a parallelogram. Find the perimeter of quadrilateral BCEF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <... | consCDL:['Shape(DO,OE,ED)', 'Shape(DA,AO,OD)', 'Shape(EO,OC,CE)', 'Shape(OA,AF,FO)', 'Shape(OF,FB,BO)', 'Shape(OB,BC,CO)', 'Collinear(AOC)', 'Collinear(EOF)', 'Collinear(BOD)', 'Collinear(DEC)', 'Collinear(AFB)'], imgCDL:['Equal(LengthOfLine(AB),4)', 'Equal(LengthOfLine(AD),3)', 'Equal(LengthOfLine(OF),3/2)'], textCDL:... | 6513 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DCE=70°, quadrilateral ABCD is a parallelogram. Find the measure of ∠DAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and th... | consCDL:['Shape(AB,BC,CD,DA)', 'Shape(DC,CE)', 'Collinear(BCE)'], imgCDL:['Equal(MeasureOfAngle(DCE),70)'], textCDL:['Equal(MeasureOfAngle(DCE),70)', 'Parallelogram(ABCD)']. | 6523 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=9, AD=6, BE bisects ∠CBA, ADCB is a parallelogram. Find DE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide a... | consCDL:['Shape(AD,DE,EB,BA)', 'Shape(BE,EC,CB)', 'Collinear(DEC)'], imgCDL:['Equal(LengthOfLine(AB),9)', 'Equal(LengthOfLine(AD),6)'], textCDL:['Equal(LengthOfLine(AB),9)', 'Equal(LengthOfLine(AD),6)', 'IsBisectorOfAngle(BE,CBA)', 'Parallelogram(ADCB)']. | 6530 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, AD=5, EO is the perpendicular bisector of BD, ADCB is a ▱. Find the perimeter of triangle CED. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <... | consCDL:['Shape(BA,AF,FO,OB)', 'Shape(BO,OE,EB)', 'Shape(EO,OD,DE)', 'Shape(CE,ED,DC)', 'Shape(OF,FD,DO)', 'Collinear(BEC)', 'Collinear(AFD)', 'Collinear(BOD)', 'Collinear(EOF)'], imgCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(AD),5)'], textCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(AD),5)', 'IsPer... | 6532 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, BC=4, EA and CD are opposite sides of the parallelogram AECD, CD is perpendicular to OD, △CBA is a right △. Find the length of line DE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based... | consCDL:['Shape(EC,CO,OE)', 'Shape(EO,OA,AE)', 'Shape(CD,DO,OC)', 'Shape(OD,DA,AO)', 'Shape(AD,DB,BA)', 'Collinear(CDB)', 'Collinear(AOC)', 'Collinear(DOE)'], imgCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(BC),4)', 'PerpendicularBetweenLine(CD,OD)'], textCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(B... | 6533 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, OE=5/2, OE is parallel to BC, quadrilateral ABCD is a ▱. Find the length of line AD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> t... | consCDL:['Shape(AB,BO,OA)', 'Shape(AO,OD,DA)', 'Shape(OB,BC,CO)', 'Shape(DO,OE,ED)', 'Shape(EO,OC,CE)', 'Collinear(AOC)', 'Collinear(BOD)', 'Collinear(CED)'], imgCDL:['Equal(LengthOfLine(OE),5/2)', 'ParallelBetweenLine(OE,BC)'], textCDL:['Equal(LengthOfLine(OE),5/2)', 'ParallelBetweenLine(OE,BC)', 'Parallelogram(ABCD)'... | 6536 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=80°, AE bisects ∠DAB, EA∥CF, quadrilateral ABCD is a ▱. Find the measure of ∠ECF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think>... | consCDL:['Shape(AB,BE,EA)', 'Shape(AE,EC,CF,FA)', 'Shape(FC,CD,DF)', 'Collinear(AFD)', 'Collinear(BEC)'], imgCDL:['Equal(MeasureOfAngle(ABC),80)', 'ParallelBetweenLine(EA,CF)'], textCDL:['Equal(MeasureOfAngle(ABC),80)', 'IsBisectorOfAngle(AE,DAB)', 'ParallelBetweenLine(EA,CF)', 'Parallelogram(ABCD)']. | 6541 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4, AD=10, AE is the angle bisector of ∠DAB, AD and BC are opposite sides of the ▱ ABCD. Find the length of line EC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You fi... | consCDL:['Shape(AB,BE,EA)', 'Shape(AE,EC,CD,DA)', 'Collinear(BEC)'], imgCDL:['Equal(LengthOfLine(AB),4)', 'Equal(LengthOfLine(AD),10)'], textCDL:['Equal(LengthOfLine(AB),4)', 'Equal(LengthOfLine(AD),10)', 'IsBisectorOfAngle(AE,DAB)', 'Parallelogram(ABCD)']. | 6569 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the perimeter of triangle ABE is 12, ABCD is a ▱, EO is perpendicular to DO. Find the perimeter of ABCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think with... | consCDL:['Shape(AB,BF,FA)', 'Shape(AF,FE,EA)', 'Shape(EF,FO,OE)', 'Shape(FB,BO,OF)', 'Shape(OB,BC,CO)', 'Shape(EO,OD,DE)', 'Shape(DO,OC,CD)', 'Collinear(AFOC)', 'Collinear(BFE)', 'Collinear(AED)', 'Collinear(BOD)'], imgCDL:['PerpendicularBetweenLine(EO,DO)'], textCDL:['Equal(PerimeterOfTriangle(ABE),12)', 'Parallelogra... | 6573 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the sum of AC and BD is 11, the sum of Perimeter(△ABO) and the perimeter of triangle AOD is 19, quadrilateral ABCD is a parallelogram. Find the perimeter of ABCD. Please provide the consCDL and imgCDL based on this given geometric diagram and prov... | consCDL:['Shape(AB,BO,OA)', 'Shape(OB,BC,CO)', 'Shape(DO,OC,CD)', 'Shape(AO,OD,DA)', 'Collinear(AOC)', 'Collinear(BOD)'], imgCDL:[], textCDL:['Equal(Add(LengthOfLine(AC),LengthOfLine(BD)),11)', 'Equal(Add(PerimeterOfTriangle(ABO),PerimeterOfTriangle(AOD)),19)', 'Parallelogram(ABCD)']. | 6582 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=AC, ∠DAE=50°, DE is the perpendicular bisector of AB. Find the measure of ∠DBC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tag... | consCDL:['Shape(AE,ED,DA)', 'Shape(EB,BD,DE)', 'Shape(DB,BC,CD)', 'Collinear(AEB)', 'Collinear(ADC)'], imgCDL:['Equal(LengthOfLine(AB),LengthOfLine(AC))', 'Equal(MeasureOfAngle(DAE),50)'], textCDL:['Equal(LengthOfLine(AB),LengthOfLine(AC))', 'Equal(MeasureOfAngle(DAE),50)', 'IsPerpendicularBisectorOfLine(DE,AB)']. | 6586 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=6, AD=5, OF=2, ABCD is a ▱. Find the perimeter of BCEF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(DA,AO,OD)', 'Shape(DO,OE,ED)', 'Shape(EO,OC,CE)', 'Shape(CO,OB,BC)', 'Shape(OA,AF,FO)', 'Shape(OF,FB,BO)', 'Collinear(DOB)', 'Collinear(EOF)', 'Collinear(AOC)', 'Collinear(DEC)', 'Collinear(AFB)'], imgCDL:['Equal(LengthOfLine(AB),6)', 'Equal(LengthOfLine(AD),5)', 'Equal(LengthOfLine(OF),2)'], textCDL:['... | 6592 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBO=52°, ⌒OAD=⌒ODC, the center of ⊙O is O, AB is the diameter of ⊙O. Find the measure of ∠BAD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think... | consCDL:['Shape(BC,OCB)', 'Shape(CD,ODC)', 'Shape(DA,OAD)', 'Shape(AB,OBA)', 'Shape(CB,BD,DC)', 'Shape(DB,BA,AD)', 'Collinear(BOA)', 'Cocircular(O,ADCB)'], imgCDL:['Equal(MeasureOfAngle(CBO),52)', 'Equal(MeasureOfArc(OAD),MeasureOfArc(ODC))'], textCDL:['Equal(MeasureOfAngle(CBO),52)', 'Equal(MeasureOfArc(OAD),MeasureOf... | 6607 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAO=40°, ∠OEC=90°, the center of circle O is O. Find ∠DBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all ... | consCDL:['Shape(AC,OCA)', 'Shape(DO,OA,OAD)', 'Shape(BD,ODB)', 'Shape(CE,EB,OBC)', 'Shape(AO,OE,EC,CA)', 'Shape(EO,OD,DE)', 'Shape(ED,DB,BE)', 'Collinear(CED)', 'Collinear(AOEB)', 'Cocircular(O,ADBC)'], imgCDL:['Equal(MeasureOfAngle(CAO),40)', 'Equal(MeasureOfAngle(OEC),90)'], textCDL:['Equal(MeasureOfAngle(CAO),40)', ... | 6616 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, Diameter(⊙O) is 6, ∠BAE=60°, O is the center of ⊙O, BD is the diameter of ⊙O. Find the length of line BC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think wit... | consCDL:['Shape(AB,OBA)', 'Shape(DE,EA,OAD)', 'Shape(CD,ODC)', 'Shape(BC,OCB)', 'Shape(BA,AE,EO,OB)', 'Shape(BO,OE,EC,CB)', 'Shape(CE,ED,DC)', 'Collinear(BOED)', 'Collinear(AEC)', 'Cocircular(O,ADCB)'], imgCDL:['Equal(MeasureOfAngle(BAE),60)'], textCDL:['Equal(DiameterOfCircle(O),6)', 'Equal(MeasureOfAngle(BAE),60)', '... | 6619 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACD=20°, the center of ⊙O is O, the diameter of circle O is AB. Find the measure of ∠DAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></th... | consCDL:['Shape(BC,OCB)', 'Shape(DE,EO,OB,OBD)', 'Shape(AD,ODA)', 'Shape(CA,OAC)', 'Shape(CB,BO,OE,EC)', 'Shape(CE,EA,AC)', 'Shape(AE,ED,DA)', 'Collinear(CED)', 'Collinear(BOEA)', 'Cocircular(O,BDAC)'], imgCDL:['Equal(MeasureOfAngle(ACD),20)'], textCDL:['Equal(MeasureOfAngle(ACD),20)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6622 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BC=3, ∠BDE=30°, O is the center of circle O, AB is the diameter of circle O. Find the length of line AB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think with... | consCDL:['Shape(CA,OAC)', 'Shape(BC,OCB)', 'Shape(DB,OBD)', 'Shape(AC,CE,EO,OA)', 'Shape(EC,CB,BE)', 'Shape(DE,EB,BD)', 'Shape(AO,OE,ED,ODA)', 'Collinear(AOEB)', 'Collinear(CED)', 'Cocircular(O,ACBD)'], imgCDL:['Equal(LengthOfLine(BC),3)', 'Equal(MeasureOfAngle(BDE),30)'], textCDL:['Equal(LengthOfLine(BC),3)', 'Equal(M... | 6629 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=55°, O is the center of ⊙O, the diameter of ⊙O is AB. Find ∠DCB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pr... | consCDL:['Shape(ODA,AD)', 'Shape(DA,AO,OM,MD)', 'Shape(DM,MB,BD)', 'Shape(DB,OBD)', 'Shape(MO,OA,OAC,CM)', 'Shape(BM,MC,CB)', 'Shape(BC,OCB)', 'Collinear(DMC)', 'Collinear(AOMB)', 'Cocircular(O,ACBD)'], imgCDL:['Equal(MeasureOfAngle(ABD),55)'], textCDL:['Equal(MeasureOfAngle(ABD),55)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6645 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAO=20°, ∠CBO=50°, O is the center of circle O. Find the measure of ∠AOB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and th... | consCDL:['Shape(OA,OAC,CM,MO)', 'Shape(AO,OM,MA)', 'Shape(MC,CB,BM)', 'Shape(AM,MB,OBA)', 'Shape(OBA,AB)', 'Shape(OCB,BC)', 'Collinear(AMC)', 'Collinear(OMB)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(CAO),20)', 'Equal(MeasureOfAngle(CBO),50)'], textCDL:['Equal(MeasureOfAngle(CAO),20)', 'Equal(MeasureOfAngle... | 6663 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=65°, O is the center of ⊙O, the diameter of circle O is AB. Find ∠DCB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and t... | consCDL:['Shape(ODA,AD)', 'Shape(DA,AO,OM,MD)', 'Shape(DM,MB,BD)', 'Shape(DB,OBD)', 'Shape(MO,OA,OAC,CM)', 'Shape(MC,CB,BM)', 'Shape(BC,OCB)', 'Collinear(AOMB)', 'Collinear(DMC)', 'Cocircular(O,ACBD)'], imgCDL:['Equal(MeasureOfAngle(ABD),65)'], textCDL:['Equal(MeasureOfAngle(ABD),65)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6689 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABO=40°, the center of ⊙O is O. Find the measure of ∠BCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(OM,MC,OCA,AO)', 'Shape(OA,AM,MO)', 'Shape(CM,MB,BC)', 'Shape(MA,AB,BM)', 'Shape(BA,OAB)', 'Shape(CB,OBC)', 'Collinear(AMC)', 'Collinear(OMB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(ABO),40)'], textCDL:['Equal(MeasureOfAngle(ABO),40)', 'IsCentreOfCircle(O,O)']. | 6694 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DBA=53°, O is the center of ⊙O, the diameter of circle O is AB. Find ∠BCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and t... | consCDL:['Shape(BD,ODB)', 'Shape(DB,BO,OE,ED)', 'Shape(DE,EA,OAD)', 'Shape(AE,EC,CA)', 'Shape(AC,OCA)', 'Shape(BC,CE,EO,OB)', 'Shape(CB,OBC)', 'Collinear(BOEA)', 'Collinear(DEC)', 'Cocircular(O,ADBC)'], imgCDL:['Equal(MeasureOfAngle(DBA),53)'], textCDL:['Equal(MeasureOfAngle(DBA),53)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6704 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAC=40°, O is the center of circle O. Find ∠BOC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(BO,OC,CB)', 'Shape(BC,OCB)', 'Shape(OB,BA,AC,CO)', 'Shape(AB,OBA)', 'Shape(CA,OAC)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(BAC),40)'], textCDL:['Equal(MeasureOfAngle(BAC),40)', 'IsCentreOfCircle(O,O)']. | 6713 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠COA=110°, O is the center of circle O, the diameter of circle O is AB. Find ∠CBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tag... | consCDL:['Shape(BA,AO,OC,CB)', 'Shape(AB,OBA)', 'Shape(BC,OCB)', 'Shape(CO,OA,OAC)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(COA),110)'], textCDL:['Equal(MeasureOfAngle(COA),110)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)']. | 6718 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAC=60°, the center of circle O is O. Find the measure of ∠BOC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide... | consCDL:['Shape(AB,OBA)', 'Shape(BA,AC,CO,OB)', 'Shape(CA,OAC)', 'Shape(BO,OC,OCB)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(BAC),60)'], textCDL:['Equal(MeasureOfAngle(BAC),60)', 'IsCentreOfCircle(O,O)']. | 6722 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAB=60°, O is the center of circle O, AB is the diameter of circle O, AD∥OC. Find ∠DAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thin... | consCDL:['Shape(AD,ODA)', 'Shape(DA,AC,OCD)', 'Shape(CO,OB,OBC)', 'Shape(AO,OC,CA)', 'Shape(BO,OA,OAB)', 'Collinear(AOB)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(DAB),60)', 'ParallelBetweenLine(AD,OC)'], textCDL:['Equal(MeasureOfAngle(DAB),60)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', 'Parall... | 6726 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=25°, ∠DEC=30°, the center of circle O is O. Find ∠DOB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all ... | consCDL:['Shape(BA,OAB)', 'Shape(AB,BF,FA)', 'Shape(AF,FE,OEA)', 'Shape(FB,BM,MF)', 'Shape(CM,MB,OBC)', 'Shape(OM,MC,CN,NO)', 'Shape(DN,NC,OCD)', 'Shape(EN,ND,DE)', 'Shape(ED,ODE)', 'Shape(EF,FM,MO,ON,NE)', 'Collinear(AFMC)', 'Collinear(BMO)', 'Collinear(DNO)', 'Collinear(ENC)', 'Collinear(BFE)', 'Cocircular(O,ABCDE)']... | 6731 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBO=19°, ∠OAC=19°, O is the center of ⊙O. Find the measure of ∠AOB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pro... | consCDL:['Shape(CA,OAC)', 'Shape(BC,OCB)', 'Shape(AO,OB,OBA)', 'Shape(AC,CO,OA)', 'Shape(OC,CB,BO)', 'Cocircular(O,CBA)'], imgCDL:['Equal(MeasureOfAngle(CBO),19)', 'Equal(MeasureOfAngle(OAC),19)'], textCDL:['Equal(MeasureOfAngle(CBO),19)', 'Equal(MeasureOfAngle(OAC),19)', 'IsCentreOfCircle(O,O)']. | 6768 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAO=35°, O is the center of ⊙O, AB is the diameter of circle O, CD is the tangent to circle O. Find the measure of ∠BCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You... | consCDL:['Shape(AD,ODA)', 'Shape(DA,AO,OD)', 'Shape(DO,OB,OBD)', 'Shape(BO,OA,OAB)', 'Shape(BC,CD,OBD)', 'Collinear(AOBC)', 'Cocircular(O,ABD)'], imgCDL:['Equal(MeasureOfAngle(DAO),35)'], textCDL:['Equal(MeasureOfAngle(DAO),35)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', 'IsTangentOfCircle(CD,O)']. | 6782 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAP=40°, O is the center of ⊙O, AP is the tangent to circle O. Find the measure of ∠APB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thi... | consCDL:['Shape(BA,AP,OBP)', 'Shape(BP,PO,OB)', 'Shape(PB,OBP)', 'Shape(BO,OP,OPB)', 'Collinear(OBA)', 'Cocircular(O,BP)'], imgCDL:['Equal(MeasureOfAngle(BAP),40)'], textCDL:['Equal(MeasureOfAngle(BAP),40)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AP,O)']. | 6783 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BOC=76°, O is the center of ⊙O, EC is the tangent to ⊙O. Find ∠BCE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pro... | consCDL:['Shape(AC,CO,OB,BA)', 'Shape(OC,CB,BO)', 'Shape(BC,OCB)', 'Shape(BC,CE)', 'Shape(AB,OBA)', 'Shape(CA,OAC)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(BOC),76)'], textCDL:['Equal(MeasureOfAngle(BOC),76)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(EC,O)']. | 6788 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABO=65°, the center of circle O is O, the tangent to ⊙O is CA. Find the measure of ∠BAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thi... | consCDL:['Shape(AO,OB,OBA)', 'Shape(OA,AB,BO)', 'Shape(BA,OAB)', 'Shape(BA,AC)', 'Cocircular(O,AB)'], imgCDL:['Equal(MeasureOfAngle(ABO),65)'], textCDL:['Equal(MeasureOfAngle(ABO),65)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(CA,O)']. | 6791 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=AC, ∠CAB=100°, CE is the angle bisector of ∠BCA, AD is the median of triangle ABC. Find ∠AFC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <thin... | consCDL:['Shape(AE,EF,FA)', 'Shape(EB,BD,DF,FE)', 'Shape(AF,FC,CA)', 'Shape(FD,DC,CF)', 'Collinear(AEB)', 'Collinear(AFD)', 'Collinear(EFC)', 'Collinear(BDC)'], imgCDL:['Equal(LengthOfLine(AB),LengthOfLine(AC))', 'Equal(MeasureOfAngle(CAB),100)'], textCDL:['Equal(LengthOfLine(AB),LengthOfLine(AC))', 'Equal(MeasureOfAng... | 6800 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BD=BC, ∠BCD=55°, ABCD is a ▱, BE⊥AE. Find the measure of ∠EAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide a... | consCDL:['Shape(DA,AE,ED)', 'Shape(EA,AB,BE)', 'Shape(CD,DE,EB,BC)', 'Collinear(DEB)'], imgCDL:['Equal(LengthOfLine(BD),LengthOfLine(BC))', 'Equal(MeasureOfAngle(BCD),55)', 'PerpendicularBetweenLine(BE,AE)'], textCDL:['Equal(LengthOfLine(BD),LengthOfLine(BC))', 'Equal(MeasureOfAngle(BCD),55)', 'Parallelogram(ABCD)', 'P... | 6818 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAB=100°, AD and BC are opposite sides of the ▱ ABCD. Find the measure of ∠DCE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags ... | consCDL:['Shape(AB,BC,CD,DA)', 'Shape(DC,CE)', 'Collinear(BCE)'], imgCDL:['Equal(MeasureOfAngle(DAB),100)'], textCDL:['Equal(MeasureOfAngle(DAB),100)', 'Parallelogram(ABCD)']. | 6838 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAE=20°, ∠ECD=35°, ∠FBE=45°. Find ∠DFE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></... | consCDL:['Shape(AF,FD,DA)', 'Shape(FB,BE,EF)', 'Shape(DF,FE,EC,CD)', 'Collinear(AFE)', 'Collinear(ADC)', 'Collinear(DFB)', 'Collinear(BEC)'], imgCDL:['Equal(MeasureOfAngle(DAE),20)', 'Equal(MeasureOfAngle(ECD),35)', 'Equal(MeasureOfAngle(FBE),45)'], textCDL:['Equal(MeasureOfAngle(DAE),20)', 'Equal(MeasureOfAngle(ECD),3... | 6847 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=60°, ∠CAB=55°. Find the measure of ∠BCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <C... | consCDL:['Shape(AB,BC,CA)'], imgCDL:['Equal(MeasureOfAngle(ABC),60)', 'Equal(MeasureOfAngle(CAB),55)'], textCDL:['Equal(MeasureOfAngle(ABC),60)', 'Equal(MeasureOfAngle(CAB),55)']. | 6851 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=CD, ∠FEB=70°, the center of circle O is O, the diameter of circle O is AB. Find ∠ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thin... | consCDL:['Shape(AD,ODA)', 'Shape(DA,AF,FD)', 'Shape(DC,OCD)', 'Shape(DF,FO,OD)', 'Shape(DO,OB,BD)', 'Shape(CD,DB,BC)', 'Shape(CB,OBC)', 'Shape(BE,OEB)', 'Shape(BF,FE,EB)', 'Shape(EF,FA,OAE)', 'Collinear(AFOB)', 'Collinear(DFE)', 'Cocircular(O,DAEBC)'], imgCDL:['Equal(LengthOfLine(AD),LengthOfLine(CD))', 'Equal(MeasureO... | 6862 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OBA=40°, the center of circle O is O. Find ∠ACB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(AO,OD,DA)', 'Shape(AD,DB,BA)', 'Shape(AB,OBA)', 'Shape(BD,DC,CB)', 'Shape(BC,OCB)', 'Shape(CD,DO,OA,OAC)', 'Collinear(ADC)', 'Collinear(ODB)', 'Cocircular(O,ACB)'], imgCDL:['Equal(MeasureOfAngle(OBA),40)'], textCDL:['Equal(MeasureOfAngle(OBA),40)', 'IsCentreOfCircle(O,O)']. | 6863 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=32°, the center of circle O is O. Find ∠AOC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(BA,OAB)', 'Shape(AB,BD,DA)', 'Shape(AD,DC,CA)', 'Shape(AC,OCA)', 'Shape(CD,DO,OC)', 'Shape(CO,OD,DB,OBC)', 'Collinear(ADO)', 'Collinear(BDC)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(ABD),32)'], textCDL:['Equal(MeasureOfAngle(ABD),32)', 'IsCentreOfCircle(O,O)']. | 6881 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAO=40°, ∠OHA=90°, O is the center of circle O. Find ∠ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all ... | consCDL:['Shape(AO,OH,HA)', 'Shape(AH,HC,OCA)', 'Shape(CH,HB,BC)', 'Shape(OBC,CB)', 'Collinear(OHC)', 'Collinear(AHB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(BAO),40)', 'Equal(MeasureOfAngle(OHA),90)'], textCDL:['Equal(MeasureOfAngle(BAO),40)', 'Equal(MeasureOfAngle(OHA),90)', 'IsCentreOfCircle(O,O)']. | 6888 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=50°, O is the center of ⊙O, AB is the diameter of ⊙O, AB and AC are the legs of the isosceles triangle ABC. Find the measure of arc ODE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based... | consCDL:['Shape(OEA,AE)', 'Shape(EA,AD,ODE)', 'Shape(AO,OB,BD,DA)', 'Shape(ODE,DC,CE)', 'Shape(OBD,DB)', 'Collinear(BDC)', 'Collinear(AOB)', 'Collinear(AEC)', 'Cocircular(O,ABDE)'], imgCDL:['Equal(MeasureOfAngle(CAB),50)'], textCDL:['Equal(MeasureOfAngle(CAB),50)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', '... | 6891 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=24°, O is the center of ⊙O, the diameter of ⊙O is AB. Find the measure of ∠CDA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> t... | consCDL:['Shape(DA,AE,ED)', 'Shape(CD,DE,EC)', 'Shape(EA,AO,OB,BE)', 'Shape(CE,EB,OBC)', 'Shape(ODA,AD)', 'Shape(OCD,DC)', 'Collinear(AOB)', 'Collinear(DEB)', 'Collinear(AEC)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(CAB),24)'], textCDL:['Equal(MeasureOfAngle(CAB),24)', 'IsCentreOfCircle(O,O)', 'IsDiameter... | 6896 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAB=74°, O is the center of ⊙O. Find the measure of ∠OBC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(AB,BO,OC,CA)', 'Shape(OB,BC,CO)', 'Shape(OCA,AC)', 'Shape(OAB,BA)', 'Shape(OBC,CB)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(CAB),74)'], textCDL:['Equal(MeasureOfAngle(CAB),74)', 'IsCentreOfCircle(O,O)']. | 6923 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ADC=25°, O is the center of circle O, the tangent to circle O is BA. Find the measure of ∠OBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think... | consCDL:['Shape(OE,ED,ODC,CO)', 'Shape(OC,CE,EO)', 'Shape(EA,AD,DE)', 'Shape(EC,OCA,AE)', 'Shape(OAD,DA)', 'Shape(CB,BA,OCA)', 'Collinear(BCO)', 'Collinear(CED)', 'Collinear(OEA)', 'Cocircular(O,CAD)'], imgCDL:['Equal(MeasureOfAngle(ADC),25)'], textCDL:['Equal(MeasureOfAngle(ADC),25)', 'IsCentreOfCircle(O,O)', 'IsTange... | 6927 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=25°, O is the center of ⊙O. Find the measure of ∠AOC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all C... | consCDL:['Shape(OAB,BA)', 'Shape(OCA,AC)', 'Shape(AB,BD,DA)', 'Shape(AD,DC,CA)', 'Shape(DO,OC,CD)', 'Shape(OD,DB,OBC,CO)', 'Collinear(ADO)', 'Collinear(BDC)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(ABC),25)'], textCDL:['Equal(MeasureOfAngle(ABC),25)', 'IsCentreOfCircle(O,O)']. | 6933 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACE=20°, O is the center of ⊙O, the diameter of circle O is AB. Find the measure of ∠BDE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></th... | consCDL:['Shape(OAC,CA)', 'Shape(OEA,AE)', 'Shape(ODE,ED)', 'Shape(OBD,DB)', 'Shape(AC,CF,FA)', 'Shape(AF,FG,GA)', 'Shape(AG,GE,EA)', 'Shape(FO,OB,BD,DG,GF)', 'Shape(GD,DE,EG)', 'Shape(OF,FC,OCB,BO)', 'Collinear(CFGE)', 'Collinear(AFOB)', 'Collinear(AGD)', 'Cocircular(O,ACBDE)'], imgCDL:['Equal(MeasureOfAngle(ACE),20)'... | 6940 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠COA=50°, O is the center of ⊙O, the tangent to ⊙O is AC. Find the measure of ∠ACD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> ta... | consCDL:['Shape(OC,OCD,DO)', 'Shape(OD,DC,CO)', 'Shape(ODC,CD)', 'Shape(DA,AC,ODC)', 'Collinear(ADO)', 'Cocircular(O,DC)'], imgCDL:['Equal(MeasureOfAngle(COA),50)'], textCDL:['Equal(MeasureOfAngle(COA),50)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AC,O)']. | 6943 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠OCA=26°, O is the center of circle O, AB is the diameter of ⊙O. Find ∠COB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and t... | consCDL:['Shape(OAB,BO,OA)', 'Shape(OC,CA,AO)', 'Shape(OB,OBC,CO)', 'Shape(OCA,AC)', 'Collinear(BOA)', 'Cocircular(O,ABC)'], imgCDL:['Equal(MeasureOfAngle(OCA),26)'], textCDL:['Equal(MeasureOfAngle(OCA),26)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)']. | 6950 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CD=2OE, the center of circle O is O, AB is the diameter of ⊙O, CE is perpendicular to OE. Find ∠DCB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <... | consCDL:['Shape(AO,OD,ODA)', 'Shape(OAC,CE,EO,OA)', 'Shape(OE,ED,DO)', 'Shape(EC,CB,BE)', 'Shape(OCB,BC)', 'Shape(EB,OBD,DE)', 'Collinear(CED)', 'Collinear(AOEB)', 'Cocircular(O,ACBD)'], imgCDL:['Equal(LengthOfLine(CD),Mul(2,LengthOfLine(OE)))', 'PerpendicularBetweenLine(CE,OE)'], textCDL:['Equal(LengthOfLine(CD),Mul(2... | 6955 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAB=80°, O is the center of circle O. Find ∠BCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(ODA,AD)', 'Shape(OCD,DC)', 'Shape(OAB,BA)', 'Shape(OBC,CB)', 'Shape(DA,AB,BC,CD)', 'Cocircular(O,ABCD)'], imgCDL:['Equal(MeasureOfAngle(DAB),80)'], textCDL:['Equal(MeasureOfAngle(DAB),80)', 'IsCentreOfCircle(O,O)']. | 6968 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FOA=40°, O is the center of circle O, the diameter of circle O is AB, E is the midpoint of ⌒OBF. Find the measure of ∠CFO. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. Y... | consCDL:['Shape(OEA,AC,CE)', 'Shape(EC,CO,OE)', 'Shape(EO,OB,BE)', 'Shape(OBE,EB)', 'Shape(OAF,FC,CA)', 'Shape(CF,FO,OC)', 'Shape(OF,OFB,BO)', 'Collinear(ACOB)', 'Collinear(FCE)', 'Cocircular(O,AFBE)'], imgCDL:['Equal(MeasureOfAngle(FOA),40)'], textCDL:['Equal(MeasureOfAngle(FOA),40)', 'IsCentreOfCircle(O,O)', 'IsDiame... | 6974 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AOB=120°, O is the center of ⊙O, the tangent to ⊙O is CA. Find the measure of ∠CAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> t... | consCDL:['Shape(OAB,BO,OA)', 'Shape(AO,OB,BA)', 'Shape(AB,BD,ODA)', 'Shape(OBD,DB)', 'Shape(ODA,DC,CA)', 'Collinear(CDB)', 'Cocircular(O,BDA)'], imgCDL:[], textCDL:['Equal(MeasureOfAngle(AOB),120)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(CA,O)']. | 6991 |
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