images images listlengths 1 1 | caption stringlengths 310 675 | cdl stringlengths 114 1.18k | proID stringlengths 1 4 | question stringlengths 310 675 | answer stringclasses 797 values |
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<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 within <CDL></CDL> tags. | 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, ∠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 within <CDL></CDL> tags. | 80 | |
<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> tags and then provide all CDLs within <CDL></CDL> tags. | 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, ∠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> tags and then provide all CDLs within <CDL></CDL> tags. | 55 | |
<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 all CDLs within <CDL></CDL> tags. | 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, ∠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 all CDLs within <CDL></CDL> tags. | 120 | |
<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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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)', 'ParallelBetweenLine(AD,OC)']. | 6726 | <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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 30 | |
<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 CDLs within <CDL></CDL> tags. | 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)'], imgCDL:['Equal(MeasureOfAngle(CAB),25)', 'Equal(MeasureOfAngle(DEC),30)'], textCDL:['Equal(MeasureOfAngle(CAB),25)', 'Equal(MeasureOfAngle(DEC),30)', 'IsCentreOfCircle(O,O)']. | 6731 | <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 CDLs within <CDL></CDL> tags. | 110 | |
<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 provide all CDLs within <CDL></CDL> tags. | 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, ∠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 provide all CDLs within <CDL></CDL> tags. | 76 | |
<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 first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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, ∠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 first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 20 | |
<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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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, ∠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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 25 | |
<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 provide all CDLs within <CDL></CDL> tags. | 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, ∠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 provide all CDLs within <CDL></CDL> tags. | 38 | |
<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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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, ∠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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 25 | |
<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 <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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(MeasureOfAngle(CAB),100)', 'IsBisectorOfAngle(CE,BCA)', 'IsMedianOfTriangle(AD,ABC)']. | 6800 | <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 <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 110 | |
<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 all CDLs within <CDL></CDL> tags. | 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)', 'PerpendicularBetweenLine(BE,AE)']. | 6818 | <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 all CDLs within <CDL></CDL> tags. | 35 | |
<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 and then provide all CDLs within <CDL></CDL> 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, ∠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 and then provide all CDLs within <CDL></CDL> tags. | 80 | |
<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></CDL> tags. | 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),35)', 'Equal(MeasureOfAngle(FBE),45)']. | 6847 | <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></CDL> tags. | 100 | |
<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 <CDL></CDL> tags. | 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, ∠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 <CDL></CDL> tags. | 65 | |
<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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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(MeasureOfAngle(FEB),70)'], textCDL:['Equal(LengthOfLine(AD),LengthOfLine(CD))', 'Equal(MeasureOfAngle(FEB),70)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)']. | 6862 | <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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 40 | |
<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 within <CDL></CDL> tags. | 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, ∠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 within <CDL></CDL> tags. | 50 | |
<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 within <CDL></CDL> tags. | 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, ∠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 within <CDL></CDL> tags. | 64 | |
<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 CDLs within <CDL></CDL> tags. | 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, ∠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 CDLs within <CDL></CDL> tags. | 25 | |
<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 on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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)', 'IsoscelesTriangle(ABC)']. | 6891 | <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 on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 50 | |
<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> tags and then provide all CDLs within <CDL></CDL> tags. | 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)', 'IsDiameterOfCircle(AB,O)']. | 6896 | <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> tags and then provide all CDLs within <CDL></CDL> tags. | 114 | |
<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 CDLs within <CDL></CDL> tags. | 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, ∠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 CDLs within <CDL></CDL> tags. | 16 | |
<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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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)', 'IsTangentOfCircle(BA,O)']. | 6927 | <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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 40 | |
<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 CDLs within <CDL></CDL> tags. | 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, ∠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 CDLs within <CDL></CDL> tags. | 50 | |
<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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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)'], textCDL:['Equal(MeasureOfAngle(ACE),20)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)']. | 6940 | <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></think> tags and then provide all CDLs within <CDL></CDL> tags. | 110 | |
<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> tags and then provide all CDLs within <CDL></CDL> tags. | 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, ∠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> tags and then provide all CDLs within <CDL></CDL> tags. | 25 | |
<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 then provide all CDLs within <CDL></CDL> tags. | 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, ∠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 then provide all CDLs within <CDL></CDL> tags. | 52 | |
<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 <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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,LengthOfLine(OE)))', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AB,O)', 'PerpendicularBetweenLine(CE,OE)']. | 6955 | <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 <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 45/2 | |
<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 within <CDL></CDL> tags. | 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, ∠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 within <CDL></CDL> tags. | 100 | |
<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. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 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)', 'IsDiameterOfCircle(AB,O)', 'IsMidpointOfArc(E,OBF)']. | 6974 | <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. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | 35 | |
<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> tags and then provide all CDLs within <CDL></CDL> tags. | 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 | <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> tags and then provide all CDLs within <CDL></CDL> tags. | 60 |
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