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TTTXXX01
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omega-combined-split-geometry_polygon

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train · 1.39k rows

id stringlengths 27 27	setting_key stringclasses 1 value	setting_name stringclasses 0 values	messages listlengths 1 1	ground_truth stringlengths 3 7	dataset stringclasses 1 value
geometry_polygon_train_0000	geometry_polygon	null	[ { "role": "user", "content": "ABCDE is a regular 5-gon with center G and circumradius 6. Let P be the reflection of point B across point G. Let F be the perpendicular bisector of segment DA. Line Y passes through point B parallel to line F. Point Q is the reflection of point D across line Y. Line X is the r...	23.53	math
geometry_polygon_train_0001	geometry_polygon	null	[ { "role": "user", "content": "ACDEFGHIJK is a regular 10-gon with center B and circumradius 3. Line Y passes through points E and H. Let N be the midpoint of segment GD. Line R is the reflection of line Y across point N. Point L is the intersection of line R and segment IH. Find the distance between points ...	2.86	math
geometry_polygon_train_0002	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFG is a regular 7-gon with center X and circumradius 12. Point K is obtained by rotating point X by angle pi/3 about point F. Let I be the midpoint of segment KG. Point J is the midpoint of segment EI. Let L be the line through points E and J. Let W be the midpoint of segm...	13.55	math
geometry_polygon_train_0003	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJK is a regular 11-gon with center R and circumradius 9. Let W be the reflection of point B across point D. Point P is the midpoint of segment AR. Point V is the midpoint of segment IP. Point Y is the reflection of point V across point R. What is the distance between p...	12.04	math
geometry_polygon_train_0004	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center O and circumradius 6. Line Y is the angle bisector of angle EHG. Line M passes through point D parallel to line Y. Point Z is the intersection of segment CH and line M. Find the distance between points Z and A. Express your an...	6.39	math
geometry_polygon_train_0005	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDE be a regular 5-gon with center Z and circumradius 10. Let M be the circumcircle of polygon ABCDE. Point Q is the reflection of point Z across point D. Let R be the midpoint of segment BQ. Let I be the inversion of point R in circle M. What is the distance between poin...	8.42	math
geometry_polygon_train_0006	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHI is a regular 9-gon with center K and circumradius 10. Point Q is the reflection of point F across point B. Let L be the rotation of point I by angle 5pi/12 around point A. Let Y be the circumcircle of polygon ABCDEFGHI. Point V is the inversion of point Q with respect...	12.11	math
geometry_polygon_train_0007	geometry_polygon	null	[ { "role": "user", "content": "BCDEFGHI is a regular octagon with center A and circumradius 10. Point L is the midpoint of segment EG. Line M is the angle bisector of angle DGL. Point K is the reflection of point D across line M. Point J is the reflection of point K across point H. Point U is the midpoint of...	23.85	math
geometry_polygon_train_0008	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFG be a regular 7-gon with center M and circumradius 1. Point K is the reflection of point D across segment BC. Point I is the midpoint of segment KG. Point X is the midpoint of segment KC. Find the length of segment IX. Express your answer as a decimal number rounded ...	0.97	math
geometry_polygon_train_0009	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDFGHIJKL be a regular 11-gon with center E and circumradius 4. Let S be the circumcircle of polygon ABCDFGHIJKL. Line Z is the angle bisector of angle CKG. Line N is the perpendicular bisector of segment EJ. Let Y be the midpoint of segment AC. Let T be the reflection of...	6.71	math
geometry_polygon_train_0010	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEF be a regular hexagon with center T and circumradius 4. Point X is the midpoint of segment DE. Let Q be the rotation of point D by angle pi/12 around point A. Let M be the angle bisector of angle TXQ. Let O be the reflection of line M through point F. Point I is the r...	3.87	math
geometry_polygon_train_0011	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJKL is a regular dodecagon with center R and circumradius 11. Let Z be the circumcircle of polygon ABCDEFGHIJKL. Let Q be the midpoint of segment IL. Let P be the inversion of point Q in circle Z. What is the distance between points Q and P? Express your answer as a de...	7.78	math
geometry_polygon_train_0012	geometry_polygon	null	[ { "role": "user", "content": "ACDEF is a regular 5-gon with center B and circumradius 2. Line J is the angle bisector of angle DBF. Let V be the reflection of line J through point A. Point T is the reflection of point C across point F. Line X passes through points T and C. Point M is the reflection of point...	5.33	math
geometry_polygon_train_0013	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJKL is a regular dodecagon with center S and circumradius 9. Point Y is obtained by rotating point A by angle pi/6 about point F. Line Q is the angle bisector of angle DLK. Let T be the reflection of line Q through point K. Point M is the reflection of point F across l...	23.29	math
geometry_polygon_train_0014	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFG is a regular 7-gon with center R and circumradius 5. Line Z is the angle bisector of angle BCF. Line S passes through point R perpendicular to line Z. Point V is the reflection of point F across line S. Point X is the midpoint of segment RD. Point I is the midpoint of s...	1.48	math
geometry_polygon_train_0015	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center Q and circumradius 1. Let R be the perpendicular bisector of segment QE. Line T is the reflection of line R across point A. Line S is the reflection of line T across point J. Line S and segment DJ intersect at point X. What is...	1.24	math
geometry_polygon_train_0016	geometry_polygon	null	[ { "role": "user", "content": "BCDEFG is a regular hexagon with center A and circumradius 2. Point L is the midpoint of segment BF. Line N is the perpendicular bisector of segment LE. Point I is the reflection of point B across line N. Find the length of segment AI. Express your answer as a decimal number ro...	3.09	math
geometry_polygon_train_0017	geometry_polygon	null	[ { "role": "user", "content": "ACDEFGHI is a regular octagon with center B and circumradius 9. Let K be the midpoint of segment HI. Point O is the reflection of point K across point G. Point L is the midpoint of segment BI. Point T is the midpoint of segment LD. Find the length of segment OT. Express your an...	19.22	math
geometry_polygon_train_0018	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center W and circumradius 4. Let X be the rotation of point G by angle 7pi/12 around point B. Let U be the line through point I parallel to segment FL. Let T be the circumcircle of polygon ABCDEFGHIJKL. Line Z passes through point A ...	5.67	math
geometry_polygon_train_0019	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJLM is a regular dodecagon with center K and circumradius 3. Point Z is the reflection of point M across point H. Let R be the line through points L and H. Let Q be the midpoint of segment ZA. Point N is the reflection of point G across line R. Find the length of segme...	2.26	math
geometry_polygon_train_0020	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center M and circumradius 9. Line Y is the angle bisector of angle LAD. Let W be the perpendicular bisector of segment CE. Let X be the reflection of line Y across line W. Line V passes through point M parallel to line Y. Point O is ...	11.15	math
geometry_polygon_train_0021	geometry_polygon	null	[ { "role": "user", "content": "ABDEFGHI is a regular octagon with center C and circumradius 5. Let M be the perpendicular bisector of segment AF. Point N is the reflection of point F across point E. Point V is the reflection of point N across line M. Find the length of segment CV. Express your answer as a de...	7.37	math
geometry_polygon_train_0022	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJKM is a regular dodecagon with center L and circumradius 8. Point U is the reflection of point C across segment MG. Segments GJ and IL intersect at point Q. Let X be the perpendicular bisector of segment AL. Point O is the reflection of point Q across line X. What is ...	13.86	math
geometry_polygon_train_0023	geometry_polygon	null	[ { "role": "user", "content": "ABCDE is a regular 5-gon with center N and circumradius 8. Line G passes through points A and C. Let V be the line through point D parallel to line G. Line Y is the reflection of line G across line V. Let U be the line through points B and N. Let S be the reflection of line Y t...	2.51	math
geometry_polygon_train_0024	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center T and circumradius 9. Point M is the midpoint of segment HB. Point X is the midpoint of segment GE. Line P passes through point X perpendicular to segment DH. Line L is the reflection of line P across point E. Point Q is the reflection ...	32.86	math
geometry_polygon_train_0025	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center X and circumradius 4. Let Y be the line through points B and K. Line Z is the reflection of line Y across point C. Point U is the intersection of line Z and segment HB. What is the distance between points U and X? Express your...	1.07	math
geometry_polygon_train_0026	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEF be a regular hexagon with center Y and circumradius 6. Point H is the midpoint of segment YE. Point N is obtained by rotating point H by angle pi/2 about point A. Point V is the midpoint of segment NB. Let P be the midpoint of segment DN. Point R is the reflection of...	20.14	math
geometry_polygon_train_0027	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEF be a regular hexagon with center I and circumradius 4. Point J is the reflection of point D across point C. Let R be the circumcircle of polygon ABCDEF. Point V is the inversion of point J with respect to circle R. Let H be the reflection of point I across point C. F...	1.05	math
geometry_polygon_train_0028	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFG is a regular 7-gon with center U and circumradius 11. Line W passes through points C and B. Point N is the reflection of point G across segment BF. Point L is the reflection of point A across line W. Find the length of segment LN. Express your answer as a decimal number...	26.75	math
geometry_polygon_train_0029	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center J and circumradius 10. Let U be the rotation of point C by angle 11pi/12 around point F. Point X is the midpoint of segment DB. Point W is the midpoint of segment FU. What is the length of segment WX? Express your answer as a decimal nu...	24.94	math
geometry_polygon_train_0030	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center R and circumradius 12. Let N be the rotation of point D by angle 2pi/3 around point F. Point V is the reflection of point K across segment ND. Let S be the angle bisector of angle LVK. Point O is the reflection of point L acro...	12.7	math
geometry_polygon_train_0031	geometry_polygon	null	[ { "role": "user", "content": "ABCDEGHIJ is a regular 9-gon with center F and circumradius 12. Line V passes through points H and C. Line S is the angle bisector of angle FJB. Line M is the reflection of line S across line V. Point P is the reflection of point F across line M. Let Q be the reflection of poin...	35.9	math
geometry_polygon_train_0032	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGH be a regular octagon with center W and circumradius 7. Point O is the midpoint of segment WD. Point K is the reflection of point O across segment WA. Let Z be the perpendicular bisector of segment WA. Point V is the reflection of point C across line Z. Find the len...	13.4	math
geometry_polygon_train_0033	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJ is a regular 10-gon with center Z and circumradius 11. Let L be the circumcircle of polygon ABCDEFGHIJ. Circle Q is the reflection of circle L across point I. Point X is the inversion of point G with respect to circle Q. Point M is the reflection of point B across po...	21.02	math
geometry_polygon_train_0034	geometry_polygon	null	[ { "role": "user", "content": "Let ABCD be a square with center P and circumradius 12. Let R be the circumcircle of polygon ABCD. Line Z is the angle bisector of angle DAP. Line N is the perpendicular bisector of segment BP. Let I be the reflection of circle R across line Z. Let H be the reflection of circle...	11.74	math
geometry_polygon_train_0035	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJKL is a regular dodecagon with center T and circumradius 6. Point U is obtained by rotating point H by angle pi/6 about point B. Let W be the angle bisector of angle UDJ. Let Z be the perpendicular bisector of segment DC. Let N be the reflection of line W across line ...	9.07	math
geometry_polygon_train_0036	geometry_polygon	null	[ { "role": "user", "content": "BCDEFG is a regular hexagon with center A and circumradius 10. Line H passes through points D and A. Let L be the reflection of line H through point C. Let W be the reflection of line L across line H. Let O be the reflection of point E across point B. Point Y is the reflection ...	55.68	math
geometry_polygon_train_0037	geometry_polygon	null	[ { "role": "user", "content": "ABDEFGHI is a regular octagon with center C and circumradius 8. Point Y is the reflection of point H across point D. Let K be the midpoint of segment FD. Point Z is the midpoint of segment GY. Let Q be the reflection of point A across point Z. What is the length of segment KQ? ...	17.29	math
geometry_polygon_train_0038	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGH be a regular octagon with center P and circumradius 7. Line I is the angle bisector of angle PDH. Line M passes through points E and C. Point V is the reflection of point F across line M. Point N is the reflection of point V across line I. What is the distance betw...	14.0	math
geometry_polygon_train_0039	geometry_polygon	null	[ { "role": "user", "content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 8. Line Y is the perpendicular bisector of segment LK. Line X is the reflection of line Y across point A. Let R be the reflection of line X across line Y. Point Z is the reflection of point E across line X. ...	59.85	math
geometry_polygon_train_0040	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJ is a regular 10-gon with center M and circumradius 12. Let R be the reflection of point C across point F. Let Q be the midpoint of segment GF. Let P be the line through points Q and J. Segment DI and line P intersect at point Y. What is the length of segment YR? Expr...	30.11	math
geometry_polygon_train_0041	geometry_polygon	null	[ { "role": "user", "content": "ABCD is a square with center O and circumradius 12. Point N is the reflection of point D across point B. Let Y be the perpendicular bisector of segment CA. Point M is the reflection of point D across segment AN. Point K is the reflection of point M across line Y. Let J be the m...	12.24	math
geometry_polygon_train_0042	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center T and circumradius 10. Let Q be the midpoint of segment LA. Let O be the line through point F parallel to segment GK. Point V is the reflection of point Q across line O. Find the length of segment VL. Express your answer as a ...	2.59	math
geometry_polygon_train_0043	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJKL is a regular dodecagon with center R and circumradius 5. Let O be the perpendicular bisector of segment LR. Line U is the reflection of line O across point C. Let M be the circumcircle of polygon ABCDEFGHIJKL. Let N be the reflection of circle M across line U. Poin...	2.11	math
geometry_polygon_train_0044	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center S and circumradius 3. Let W be the circumcircle of polygon ABCDEFGHIJKL. Let Z be the angle bisector of angle HCD. Circle Y is the reflection of circle W across line Z. Line T is the perpendicular bisector of segment SK. Let P...	13.28	math
geometry_polygon_train_0045	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDFGHIJ be a regular 9-gon with center E and circumradius 10. Let N be the rotation of point A by angle 11pi/12 around point J. Point L is the reflection of point B across point N. Let S be the angle bisector of angle GCJ. Point Y is the reflection of point L across line ...	42.57	math
geometry_polygon_train_0046	geometry_polygon	null	[ { "role": "user", "content": "EM = 8. ABCDFGHIJKL is a regular 11-gon with center M and circumradius 7. Line O is the perpendicular bisector of segment JI. Point Z is the midpoint of segment GC. Line T passes through point D perpendicular to line O. Line V passes through point K perpendicular to line T. Poi...	8.16	math
geometry_polygon_train_0047	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGH be a regular octagon with center I and circumradius 8. Let L be the line through points G and I. Let T be the midpoint of segment BG. Point S is the reflection of point D across point F. Let Z be the perpendicular bisector of segment BT. Let V be the line through p...	13.39	math
geometry_polygon_train_0048	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDE be a regular 5-gon with center Q and circumradius 8. Let X be the reflection of point Q across point A. Let H be the angle bisector of angle QXB. Point O is the reflection of point C across line H. Let M be the midpoint of segment EO. What is the distance between poin...	9.72	math
geometry_polygon_train_0049	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center X and circumradius 2. Let Y be the line through points C and G. Line K passes through points H and X. Let S be the reflection of line Y through point E. Lines K and S intersect at point Q. What is the length of segment QA? Express your ...	7.21	math
geometry_polygon_train_0050	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEF be a regular hexagon with center R and circumradius 1. Let J be the line through points B and D. Segment CF and line J intersect at point W. Let N be the midpoint of segment AW. Find the length of segment FN. Express your answer as a decimal number rounded to 2 decim...	1.09	math
geometry_polygon_train_0051	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGIJKLM is a regular dodecagon with center H and circumradius 5. Let Q be the circumcircle of polygon ABCDEFGIJKLM. Let X be the midpoint of segment MJ. Let S be the reflection of circle Q through point D. Point R is the reflection of point K across point X. Let Z be the i...	15.29	math
geometry_polygon_train_0052	geometry_polygon	null	[ { "role": "user", "content": "Let ABCD be a square with center Q and circumradius 9. Let Z be the circumcircle of polygon ABCD. Let O be the midpoint of segment BA. Let V be the reflection of circle Z through point B. Point W is the inversion of point O with respect to circle V. Point M is the reflection of...	16.6	math
geometry_polygon_train_0053	geometry_polygon	null	[ { "role": "user", "content": "Let BCDEFGHI be a regular octagon with center A and circumradius 3. Point U is the reflection of point C across point I. Let K be the midpoint of segment FA. Let X be the line through point K parallel to segment BE. Point P is the reflection of point H across line X. Find the l...	7.44	math
geometry_polygon_train_0054	geometry_polygon	null	[ { "role": "user", "content": "ABCEF is a regular 5-gon with center D and circumradius 2. Let K be the rotation of point B by angle 11pi/12 around point C. Point M is the reflection of point C across point K. Point T is the reflection of point F across point E. Point O is the reflection of point M across seg...	3.47	math
geometry_polygon_train_0055	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDE be a regular 5-gon with center U and circumradius 10. Line Z passes through points D and C. Let X be the line through point E parallel to line Z. Line Q is the reflection of line X across line Z. Point G is the midpoint of segment CD. Point V is the reflection of poin...	23.12	math
geometry_polygon_train_0056	geometry_polygon	null	[ { "role": "user", "content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 11. Let X be the reflection of point K across point J. Let Z be the perpendicular bisector of segment IK. Line R passes through points M and X. Let Y be the reflection of line R across line Z. Point S is the...	10.2	math
geometry_polygon_train_0057	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJK be a regular 11-gon with center Q and circumradius 8. Line N is the perpendicular bisector of segment GF. Line O is the angle bisector of angle JQA. Let P be the line through point I parallel to line O. Line Z passes through point C parallel to line P. Let L be ...	2.86	math
geometry_polygon_train_0058	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEF be a regular hexagon with center Q and circumradius 8. Line Z is the angle bisector of angle DFE. Let L be the perpendicular bisector of segment DE. Let Y be the rotation of point F by angle pi/12 around point A. Let I be the reflection of line Z across line L. Let R...	43.06	math
geometry_polygon_train_0059	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center S and circumradius 9. Line T is the angle bisector of angle CAF. Point U is the reflection of point H across line T. Let Z be the circumcircle of polygon ABCDEFGH. Circle L is the reflection of circle Z across point U. Point X is the in...	14.2	math
geometry_polygon_train_0060	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFG be a regular 7-gon with center Q and circumradius 9. Let M be the circumcircle of polygon ABCDEFG. Let P be the reflection of circle M through point F. Point H is the inversion of point A with respect to circle P. Point J is the inversion of point G with respect to ...	19.12	math
geometry_polygon_train_0061	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFG be a regular 7-gon with center P and circumradius 10. Point O is obtained by rotating point C by angle pi about point B. Line R passes through point C perpendicular to segment CG. Line Y passes through point E parallel to line R. Let Q be the circumcircle of polygon...	16.38	math
geometry_polygon_train_0062	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJ is a regular 10-gon with center Y and circumradius 4. Let M be the circumcircle of polygon ABCDEFGHIJ. Circle V is the reflection of circle M across point G. Let N be the reflection of point C across point B. Point L is the inversion of point N with respect to circle...	6.61	math
geometry_polygon_train_0063	geometry_polygon	null	[ { "role": "user", "content": "ABCDEGHIJ is a regular 9-gon with center F and circumradius 4. Let U be the perpendicular bisector of segment CD. Line T is the reflection of line U across point D. Let N be the line through point I perpendicular to line T. Point Q is the reflection of point A across line N. Fi...	0.94	math
geometry_polygon_train_0064	geometry_polygon	null	[ { "role": "user", "content": "Let ABCD be a square with center W and circumradius 10. Line H is the angle bisector of angle DBW. Line Y passes through points W and A. Line N passes through point A parallel to line H. Point U is the midpoint of segment WC. Point F is the reflection of point B across line N. ...	26.93	math
geometry_polygon_train_0065	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center I and circumradius 8. Line P is the perpendicular bisector of segment CI. Point Q is the reflection of point D across line P. Let N be the midpoint of segment DQ. Point R is the midpoint of segment QC. Find the length of segment RN. Exp...	3.06	math
geometry_polygon_train_0066	geometry_polygon	null	[ { "role": "user", "content": "BCDEFGHIJKLM is a regular dodecagon with center A and circumradius 12. Let S be the line through points M and J. Line Z is the perpendicular bisector of segment GF. Let T be the reflection of line Z through point E. Lines S and T intersect at point Y. What is the distance betwe...	34.13	math
geometry_polygon_train_0067	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center W and circumradius 12. Point N is on segment EG. Let Y be the perpendicular bisector of segment GB. Point L is the reflection of point N across line Y. What is the measure of angle ENL, in radians? Express your answer as a decimal numbe...	1.18	math
geometry_polygon_train_0068	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center X and circumradius 10. Let S be the angle bisector of angle XHE. Let J be the midpoint of segment FA. Point N is the reflection of point X across line S. Point T is the midpoint of segment NJ. Find the distance between points T and C. E...	13.39	math
geometry_polygon_train_0069	geometry_polygon	null	[ { "role": "user", "content": "ABCDE is a regular 5-gon with center G and circumradius 11. Let F be the rotation of point A by angle pi/3 around point G. Point K is the midpoint of segment DF. Point X is the reflection of point B across point K. Point O is the midpoint of segment FX. Point H is the reflectio...	20.71	math
geometry_polygon_train_0070	geometry_polygon	null	[ { "role": "user", "content": "ABCD is a square with center W and circumradius 9. Let I be the circumcircle of polygon ABCD. Let T be the reflection of circle I through point D. Let X be the midpoint of segment WB. Point G is the inversion of point X with respect to circle T. Find the length of segment GW. E...	14.4	math
geometry_polygon_train_0071	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHJK be a regular 10-gon with center I and circumradius 4. Line O passes through points H and B. Let P be the line through point K parallel to segment JE. Lines P and O intersect at point S. What is the length of segment SG? Express your answer as a decimal number rou...	5.31	math
geometry_polygon_train_0072	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHI is a regular 9-gon with center S and circumradius 11. Let N be the perpendicular bisector of segment ID. Point M is the midpoint of segment CD. Let X be the line through point M parallel to line N. Segment ID and line X intersect at point Y. Find the distance between ...	17.65	math
geometry_polygon_train_0073	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKM be a regular dodecagon with center L and circumradius 7. Let Z be the midpoint of segment DC. Point V is the reflection of point Z across segment MF. Find the length of segment ZV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent ...	13.06	math
geometry_polygon_train_0074	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFG is a regular 7-gon with center R and circumradius 11. Let O be the line through points A and C. Point Y is the reflection of point F across line O. Point V is the reflection of point Y across segment BC. What is the distance between points V and B? Express your answer a...	13.5	math
geometry_polygon_train_0075	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJKL is a regular dodecagon with center X and circumradius 10. Point Y is the reflection of point G across point E. Let P be the midpoint of segment XA. Point S is obtained by rotating point P by angle 3pi/4 about point F. Point M is the reflection of point E across poi...	7.44	math
geometry_polygon_train_0076	geometry_polygon	null	[ { "role": "user", "content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 2. Let X be the line through points I and G. Let Q be the angle bisector of angle KFM. Let Y be the reflection of line X across line Q. Point R is the reflection of point G across line Y. What is the distance be...	5.29	math
geometry_polygon_train_0077	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGH be a regular octagon with center I and circumradius 11. Let K be the circumcircle of polygon ABCDEFGH. Let Z be the reflection of circle K through point B. Point J is the midpoint of segment FA. Point Q is the inversion of point I with respect to circle Z. Point O ...	13.56	math
geometry_polygon_train_0078	geometry_polygon	null	[ { "role": "user", "content": "ABCDFGHI is a regular octagon with center E and circumradius 3. Line R passes through points C and D. Line Y passes through point G parallel to segment HF. Point P is the intersection of lines R and Y. What is the length of segment HP? Express your answer as a decimal number ro...	6.42	math
geometry_polygon_train_0079	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFG is a regular 7-gon with center Y and circumradius 4. Line K is the perpendicular bisector of segment YF. Point I is the reflection of point C across line K. Let U be the line through points G and A. Let W be the line through point I perpendicular to line U. Point O is t...	15.6	math
geometry_polygon_train_0080	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHI is a regular 9-gon with center Z and circumradius 5. Line P passes through point B perpendicular to segment GE. Point M lies on line P. Let W be the reflection of point F across point D. Find the measure of angle WBM, in radians. Express your answer as a decimal numbe...	1.4	math
geometry_polygon_train_0081	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJK be a regular 11-gon with center T and circumradius 7. Let N be the perpendicular bisector of segment FI. Point Z is the reflection of point A across point C. Line R is the reflection of line N across point I. Line U is the perpendicular bisector of segment IJ. L...	15.48	math
geometry_polygon_train_0082	geometry_polygon	null	[ { "role": "user", "content": "ABCDEF is a regular hexagon with center L and circumradius 12. Let K be the circumcircle of polygon ABCDEF. Point O is the midpoint of segment FL. Let H be the inversion of point O in circle K. Point R is the reflection of point L across point C. What is the distance between po...	48.0	math
geometry_polygon_train_0083	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGIJK is a regular 10-gon with center H and circumradius 10. Line V is the angle bisector of angle GEI. Let U be the midpoint of segment BD. Let P be the line through point F perpendicular to line V. Point X is the reflection of point U across line P. Find the length of se...	15.48	math
geometry_polygon_train_0084	geometry_polygon	null	[ { "role": "user", "content": "Let ABDEFG be a regular hexagon with center C and circumradius 2. Point R is obtained by rotating point A by angle pi/12 about point G. Point W is obtained by rotating point B by angle pi/12 about point A. Let T be the circumcircle of polygon ABDEFG. Let O be the perpendicular ...	18.8	math
geometry_polygon_train_0085	geometry_polygon	null	[ { "role": "user", "content": "ABCDE is a regular 5-gon with center R and circumradius 9. Let U be the circumcircle of polygon ABCDE. Let M be the reflection of circle U through point A. Let J be the perpendicular bisector of segment RB. Let T be the reflection of circle M across line J. Point L is the midpo...	5.03	math
geometry_polygon_train_0086	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center Y and circumradius 5. Let O be the reflection of point C across point A. Let Q be the perpendicular bisector of segment OY. Line R is the reflection of line Q across point F. Let V be the line through point Y parallel to line R. Point M...	11.86	math
geometry_polygon_train_0087	geometry_polygon	null	[ { "role": "user", "content": "ABCDEF is a regular hexagon with center Z and circumradius 11. Line S is the angle bisector of angle ACB. Let M be the circumcircle of polygon ABCDEF. Let U be the reflection of circle M across line S. Let N be the inversion of point F in circle U. Find the length of segment NF...	19.68	math
geometry_polygon_train_0088	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGHIJKL be a regular dodecagon with center S and circumradius 10. Line Q passes through point C parallel to segment FJ. Point Z is the reflection of point L across line Q. Point P is the midpoint of segment EZ. What is the distance between points K and P? Express your ...	12.32	math
geometry_polygon_train_0089	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEFGH be a regular octagon with center R and circumradius 10. Line Y is the perpendicular bisector of segment CB. Let W be the line through point F parallel to line Y. Point U is the intersection of line W and segment AE. Find the distance between points U and D. Express...	7.65	math
geometry_polygon_train_0090	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDE be a regular 5-gon with center X and circumradius 12. Let N be the line through points B and E. Let J be the line through point X parallel to line N. Point I is the midpoint of segment AC. Let U be the line through point D parallel to line J. Let H be the reflection o...	46.17	math
geometry_polygon_train_0091	geometry_polygon	null	[ { "role": "user", "content": "ABCEF is a regular 5-gon with center D and circumradius 10. Point T is the reflection of point B across point D. Line N is the perpendicular bisector of segment TB. Point M is the reflection of point C across segment BA. Let Z be the line through point F perpendicular to line N...	1.89	math
geometry_polygon_train_0092	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEF be a regular hexagon with center L and circumradius 4. Let H be the circumcircle of polygon ABCDEF. Let P be the midpoint of segment DL. Point I is the inversion of point P with respect to circle H. Point V is the midpoint of segment CD. What is the distance between ...	5.29	math
geometry_polygon_train_0093	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGHIJKL is a regular dodecagon with center X and circumradius 5. Let S be the reflection of point K across point C. Let O be the angle bisector of angle SGE. Line T is the reflection of line O across point J. Point N is the reflection of point E across line T. Find the dis...	24.18	math
geometry_polygon_train_0094	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFGH is a regular octagon with center L and circumradius 3. Let N be the line through point E perpendicular to segment BE. Point T is the reflection of point G across segment BE. Point X is the reflection of point T across line N. Find the length of segment LX. Express your...	6.71	math
geometry_polygon_train_0095	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDFGHIJK be a regular 10-gon with center E and circumradius 9. Let V be the reflection of point I across point B. Let T be the perpendicular bisector of segment EV. Let U be the angle bisector of angle CIV. Let Q be the reflection of line T through point I. Let Z be the r...	25.45	math
geometry_polygon_train_0096	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEF be a regular hexagon with center M and circumradius 9. Point L is the reflection of point M across point A. Point G is the reflection of point B across point F. Let N be the midpoint of segment GL. Let X be the midpoint of segment EM. What is the distance between poi...	15.59	math
geometry_polygon_train_0097	geometry_polygon	null	[ { "role": "user", "content": "ABCDEFG is a regular 7-gon with center I and circumradius 9. Let T be the perpendicular bisector of segment ID. Line M is the reflection of line T across point E. Let Y be the circumcircle of polygon ABCDEFG. Let Z be the reflection of circle Y through point C. Let N be the mid...	9.23	math
geometry_polygon_train_0098	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDEF be a regular hexagon with center P and circumradius 7. Point Q is the reflection of point D across point C. Let T be the reflection of point Q across point E. Let I be the midpoint of segment CQ. Point V is the reflection of point P across segment IT. Find the distan...	12.76	math
geometry_polygon_train_0099	geometry_polygon	null	[ { "role": "user", "content": "Let ABCDE be a regular 5-gon with center S and circumradius 9. Let J be the angle bisector of angle CDE. Line O is the perpendicular bisector of segment EB. Line M is the reflection of line J across line O. Point U is the reflection of point B across point C. Let Q be the line ...	39.71	math

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