messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
value |
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[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center M and circumradius 9. Let Q be the perpendicular bisector of segment CE. Let Y be the reflection of point C across point G. Let N be the reflection of line Q through point K. Line T is the reflection of line N across line Q. Point U is the reflec... | 27.16 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center Q and circumradius 8. Let H be the midpoint of segment ED. Line K passes through points A and D. Let N be the line through point E perpendicular to line K. Let S be the reflection of point H across point E. Let W be the perpendicular bisector of segment HG. L... | 0.91 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center R and circumradius 3. Let T be the midpoint of segment DA. Let N be the angle bisector of angle FET. Point I is the reflection of point D across line N. Point P is the reflection of point I across segment DA. What is the distance between points P and H... | 8.97 | MATH |
[
{
"content": "ABCE is a square with center D and circumradius 7. Point P lies on segment CA. Line H is the perpendicular bisector of segment BP. Point S is the reflection of point D across line H. Line O passes through point S parallel to line H. Point Q is the reflection of point P across line O. What is the d... | 7.0 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center P and circumradius 4. Let K be the rotation of point C by angle pi around point G. Point V is the midpoint of segment KG. Point N is the reflection of point P across point V. Line O passes through point N perpendicular to segment HK. Let I be the line thro... | 3.55 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center V and circumradius 3. Point U is on segment BA. Let G be the line through point F perpendicular to segment BA. Point Y is the reflection of point U across point V. Point M is the reflection of point U across line G. What is the distance between points Y and ... | 7.94 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center T and circumradius 8. Point X is obtained by rotating point C by angle pi/6 about point F. Line W is the perpendicular bisector of segment AF. Line P is the reflection of line W across point C. Line K passes through point D perpendicular to line P. Point Y ... | 3.84 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center Q and circumradius 9. Let V be the line through points B and J. Let L be the rotation of point D by angle 5pi/6 around point C. Line N passes through points L and K. Let O be the line through points A and H. Lines V and N intersect at point P. Point ... | 6.03 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 7. Let Z be the line through points C and F. Let O be the circumcircle of polygon ABCDEF. Line W passes through point D parallel to line Z. Circle P is the reflection of circle O across line W. Point Y is the inversion of point F with resp... | 12.62 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center M and circumradius 1. Let X be the midpoint of segment MH. Let J be the midpoint of segment XA. Point Y is the reflection of point D across point E. Let Q be the midpoint of segment EY. Find the distance between points Q and J. Express your answer as a dec... | 1.83 | MATH |
[
{
"content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 5. Line Y is the angle bisector of angle MBH. Point X is the midpoint of segment JH. Point S is the reflection of point K across line Y. Point T is the midpoint of segment SX. Find the length of segment TL. Express your answer ... | 5.46 | MATH |
[
{
"content": "Let ABCD be a square with center F and circumradius 12. Point U is the midpoint of segment CD. Point L is the reflection of point U across point B. Let I be the rotation of point L by angle pi around point U. Point E is the midpoint of segment LF. Point K is the reflection of point I across point ... | 54.32 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center H and circumradius 4. Let G be the reflection of point E across point D. Let J be the perpendicular bisector of segment GF. Line I is the angle bisector of angle HCF. Let W be the reflection of line J across line I. Let X be the reflection of line W acro... | 2.28 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Q and circumradius 1. Let K be the circumcircle of polygon ABCDEFGH. Let W be the midpoint of segment QC. Let N be the perpendicular bisector of segment DW. Circle Y is the reflection of circle K across line N. Let V be the inversion of point G in circle Y... | 0.93 | MATH |
[
{
"content": "ABCDFG is a regular hexagon with center E and circumradius 10. Line P passes through point C parallel to segment AB. Let Q be the midpoint of segment AB. Point J is the reflection of point Q across line P. What is the distance between points D and J? Express your answer as a decimal number rounded... | 5.0 | MATH |
[
{
"content": "Let ABCDEFGHIJLM be a regular dodecagon with center K and circumradius 2. Let V be the rotation of point L by angle pi/6 around point E. Point T is the reflection of point I across point C. Let W be the perpendicular bisector of segment ML. Let S be the reflection of line W through point V. Point ... | 5.38 | MATH |
[
{
"content": "Let ABCDEFH be a regular 7-gon with center G and circumradius 8. Point K is the midpoint of segment AD. Point L is the reflection of point F across point H. Let V be the line through points L and K. Let Q be the reflection of line V through point E. Point N is the reflection of point D across line... | 35.18 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center R and circumradius 3. Let T be the vector from point E to point J. Point Z is the translation of point A by vector T. Let V be the midpoint of segment IE. Line S passes through points J and A. Let Q be the circumcircle of polygon ABCDEFGHIJ. Point Y is th... | 7.18 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center U and circumradius 4. Point Y is the midpoint of segment IU. Segments CG and EI intersect at point X. What is the distance between points X and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex... | 3.06 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center T and circumradius 5. Let V be the line through points B and T. Let J be the rotation of point E by angle pi/3 around point G. Let O be the midpoint of segment DJ. Line L passes through point E perpendicular to line V. Point U is the reflection of point... | 13.7 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center U and circumradius 5. Let S be the line through points K and L. Point O is the reflection of point E across line S. Point Z is the reflection of point F across segment OB. What is the length of segment HZ? Express your answer as a decimal number roun... | 18.03 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Y and circumradius 1. Let X be the angle bisector of angle LEH. Point V is the reflection of point L across line X. Line U passes through points A and B. Line M is the reflection of line U across point H. Point Q is the reflection of point K acro... | 4.84 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center X and circumradius 7. Line W is the angle bisector of angle DHE. Point K is the reflection of point E across line W. Let S be the midpoint of segment KG. Point R is the reflection of point H across point S. What is the length of segment HR? Express your... | 15.1 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center V and circumradius 2. Point Z is the midpoint of segment GD. Let W be the reflection of point C across point G. Line O is the angle bisector of angle ZWH. Let J be the midpoint of segment CB. Point Q is the midpoint of segment HJ. Point N is the reflec... | 2.1 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center W and circumradius 9. Line V is the angle bisector of angle IGE. Let T be the line through point A perpendicular to line V. Point X is the reflection of point F across line T. Point U is the reflection of point X across line V. Find the length of segment DU... | 17.73 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Q and circumradius 1. Let P be the midpoint of segment AC. Let U be the midpoint of segment DB. Let T be the midpoint of segment UP. What is the length of segment ET? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer ... | 1.39 | MATH |
[
{
"content": "ACDEF is a regular 5-gon with center B and circumradius 12. Let Y be the reflection of point F across point C. Let V be the perpendicular bisector of segment BA. Line G is the reflection of line V across point Y. Point Q is the reflection of point C across line G. Find the length of segment QF. Ex... | 23.28 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center W and circumradius 8. Point Q is the midpoint of segment HC. Point S is the reflection of point D across point F. Let K be the circumcircle of polygon ABCDEFGH. Point N is the inversion of point S with respect to circle K. Point Z is the midpoint of se... | 0.57 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center L and circumradius 6. Let O be the circumcircle of polygon ABCDEFGH. Let S be the angle bisector of angle FAB. Circle P is the reflection of circle O across line S. Let Z be the inversion of point B in circle P. What is the distance between points E an... | 22.64 | MATH |
[
{
"content": "Let ABCDEFGIJKLM be a regular dodecagon with center H and circumradius 2. Let R be the circumcircle of polygon ABCDEFGIJKLM. Circle Q is the reflection of circle R across point B. Let Y be the line through point M perpendicular to segment BI. Let P be the reflection of circle Q across line Y. Let ... | 1.83 | MATH |
[
{
"content": "Let ABCDEFHIJ be a regular 9-gon with center G and circumradius 1. Line Y passes through point A parallel to segment EF. Point L is the reflection of point D across line Y. Let Z be the reflection of point G across point L. Line R is the angle bisector of angle GFI. Point P is the reflection of po... | 5.55 | MATH |
[
{
"content": "ABCD is a square with center Y and circumradius 9. Let E be the perpendicular bisector of segment CY. Let Z be the reflection of line E through point C. Let T be the line through points C and B. Point S is the intersection of lines Z and T. Find the distance between points D and S. Express your an... | 14.23 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center U and circumradius 6. Let J be the circumcircle of polygon ABCDEFG. Line R is the angle bisector of angle CGE. Line L passes through point E parallel to line R. Line O is the reflection of line R across line L. Let Q be the reflection of circle J across line ... | 23.43 | MATH |
[
{
"content": "BCDEFGH is a regular 7-gon with center A and circumradius 12. Let Y be the midpoint of segment GC. Line L passes through point Y parallel to segment ED. Point I is the reflection of point B across line L. Point X is the reflection of point I across segment ED. Point U is the reflection of point X ... | 36.69 | MATH |
[
{
"content": "BCDEFG is a regular hexagon with center A and circumradius 4. Let Q be the line through point G parallel to segment CE. Point V is the reflection of point B across segment CE. Line K passes through points E and V. Lines Q and K intersect at point R. Find the distance between points R and E. Expres... | 12.0 | MATH |
[
{
"content": "Let ABCDEFGHIKLM be a regular dodecagon with center J and circumradius 6. Let P be the reflection of point I across point H. Let Q be the midpoint of segment MP. Point Z is the midpoint of segment IB. Find the distance between points Q and Z. Express your answer as a decimal number rounded to 2 de... | 2.34 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center T and circumradius 4. Line O is the angle bisector of angle DIE. Point V is the reflection of point G across line O. Let N be the midpoint of segment GB. What is the distance between points N and V? Express your answer as a decimal number rounded to ... | 2.17 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center L and circumradius 11. Let P be the line through points A and B. Line Y passes through point F parallel to line P. Let W be the reflection of line Y across line P. Point K is the reflection of point A across line W. What is the distance between points L and K... | 43.71 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Q and circumradius 6. Let M be the reflection of point D across point E. Let Z be the midpoint of segment QC. Let G be the angle bisector of angle ZAQ. Point U is the reflection of point Z across line G. What is the distance between points U and M? Expre... | 10.57 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center G and circumradius 6. Let X be the circumcircle of polygon ABCDEF. Point I is the midpoint of segment FE. Let H be the inversion of point I in circle X. What is the length of segment CH? Express your answer as a decimal number rounded to 2 decimal places... | 12.49 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center M and circumradius 4. Point W is the reflection of point C across point M. Let T be the line through point M perpendicular to segment AF. Point V is the reflection of point W across line T. Find the measure of angle EVB, in radians. Express your answer as... | 1.35 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center L and circumradius 1. Let O be the circumcircle of polygon ABCDEFGHI. Point V is the reflection of point E across segment HB. Point U is the inversion of point V with respect to circle O. Find the length of segment AU. Express your answer as a decimal numbe... | 0.56 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Q and circumradius 5. Point X is the reflection of point Q across point D. Line V passes through points X and Q. Point L is the midpoint of segment AX. Point N is the reflection of point L across line V. Find the length of segment XN. Express your answer as... | 7.17 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center R and circumradius 8. Line W is the angle bisector of angle ECF. Point O is the midpoint of segment RD. Let J be the perpendicular bisector of segment RD. Point V lies on line J. Let M be the line through point O perpendicular to line W. Point P is the refle... | 0.26 | MATH |
[
{
"content": "Let ABCD be a square with center U and circumradius 1. Line T passes through point C perpendicular to segment CA. Point L is the reflection of point D across line T. Line H is the perpendicular bisector of segment LC. Point R is the reflection of point B across line H. What is the distance between... | 3.16 | MATH |
[
{
"content": "Let ABCDF be a regular 5-gon with center E and circumradius 10. Let I be the midpoint of segment BC. Point J is the midpoint of segment IF. Let M be the circumcircle of polygon ABCDF. Point T is the inversion of point J with respect to circle M. Find the distance between points T and F. Express yo... | 94.72 | MATH |
[
{
"content": "Let BCDEF be a regular 5-gon with center A and circumradius 9. Let R be the perpendicular bisector of segment FA. Point Q is obtained by rotating point D by angle 11pi/12 about point E. Let N be the line through points D and B. Line J is the reflection of line R across point Q. Line T is the refle... | 6.87 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center J and circumradius 12. Line P is the angle bisector of angle JFE. Let U be the line through point B parallel to line P. Let T be the angle bisector of angle CAE. Line Y is the reflection of line T across line U. Point I is on line P. Line V is the reflection... | 0.52 | MATH |
[
{
"content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 3. Let S be the midpoint of segment LB. Let U be the line through point L perpendicular to segment LB. V is constructed so that KV = 6. Point O is on line U with |OV| = 3. Let W be the circumcircle of polygon ABCEFGHIJKLM. Let P be... | 5.05 | MATH |
[
{
"content": "ABCD is a square with center H and circumradius 10. Let Q be the vector from point C to point A. Point O is the translation of point D by vector Q. Let T be the perpendicular bisector of segment HB. Let V be the angle bisector of angle DCO. Let I be the reflection of line V through point D. Let Y ... | 1.14 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Z and circumradius 7. Line S passes through points I and H. Let X be the perpendicular bisector of segment DJ. Line P is the reflection of line S across line X. Line O passes through points B and J. Lines P and O intersect at point M. Find the di... | 45.79 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center X and circumradius 3. Point V is the reflection of point G across point E. Line Z passes through points D and V. Line Z and segment AX intersect at point M. What is the distance between points J and M? Express your answer as a decimal number rounded t... | 2.38 | MATH |
[
{
"content": "Let ACDEFGHI be a regular octagon with center B and circumradius 11. Let L be the reflection of point A across point C. Point V is the midpoint of segment DI. Point T is the midpoint of segment VD. What is the length of segment LT? Express your answer as a decimal number rounded to 2 decimal place... | 9.61 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center W and circumradius 6. Point N is the midpoint of segment FE. Let J be the midpoint of segment BN. What is the length of segment FJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 5.41 | MATH |
[
{
"content": "Let BCDEFGHIJKLM be a regular dodecagon with center A and circumradius 9. Let R be the midpoint of segment LI. Line U is the perpendicular bisector of segment IM. Let Q be the line through point J parallel to line U. Point V is the reflection of point D across line Q. What is the distance between ... | 18.3 | MATH |
[
{
"content": "ABCEFGHI is a regular octagon with center D and circumradius 3. Let T be the perpendicular bisector of segment DG. Let W be the line through point I perpendicular to line T. Point J is the reflection of point E across point H. Point U is the reflection of point H across line W. Let L be the midpoi... | 5.49 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center R and circumradius 12. Let M be the reflection of point E across point R. Let W be the perpendicular bisector of segment MF. Line J passes through point D parallel to line W. Point P is the reflection of point F across line J. Let I be the midpoint of segment... | 8.57 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center I and circumradius 2. Let W be the midpoint of segment GA. Point V is the midpoint of segment HA. Let T be the perpendicular bisector of segment VD. Point X is the reflection of point G across line T. Point S is the reflection of point I across segment BW.... | 4.27 | MATH |
[
{
"content": "ABCDEFHI is a regular octagon with center G and circumradius 6. Let R be the circumcircle of polygon ABCDEFHI. Let T be the reflection of circle R through point E. Let V be the inversion of point A in circle T. Point P is the midpoint of segment VE. What is the measure of angle PAB, in radians? Ex... | 1.18 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center X and circumradius 6. Line Z is the angle bisector of angle ABD. Let V be the line through point D parallel to line Z. Let K be the line through point A parallel to line V. Point R is the reflection of point C across line K. What is the distance between points ... | 21.71 | MATH |
[
{
"content": "Let ABDEFGHIJKL be a regular 11-gon with center C and circumradius 9. Let Q be the midpoint of segment FA. Point W is the reflection of point Q across segment IH. Point R is the reflection of point C across point F. Find the distance between points R and W. Express your answer as a decimal number ... | 23.84 | MATH |
[
{
"content": "Let ABDEFGHI be a regular octagon with center C and circumradius 6. Line S is the perpendicular bisector of segment DF. Point W is the midpoint of segment EB. Point R is the reflection of point W across line S. Find the length of segment RA. Express your answer as a decimal number rounded to 2 dec... | 10.24 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Y and circumradius 10. Let O be the circumcircle of polygon ABCDEFGH. Line U passes through points A and C. Point J is the reflection of point D across line U. Point T is the inversion of point J with respect to circle O. Line R passes through point D para... | 9.88 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center R and circumradius 12. Let M be the circumcircle of polygon ABCDEFGHIJKL. Circle O is the reflection of circle M across point A. Line P passes through points H and K. Point X is the reflection of point F across line P. Let Y be the inversion of p... | 20.98 | MATH |
[
{
"content": "Let ABCDEFGHJKLM be a regular dodecagon with center I and circumradius 3. Let Z be the circumcircle of polygon ABCDEFGHJKLM. Let R be the reflection of circle Z through point H. Line Q passes through points F and K. Circle U is the reflection of circle R across line Q. Point P is the reflection of... | 9.36 | MATH |
[
{
"content": "Let ABCDFGH be a regular 7-gon with center E and circumradius 11. Line Q passes through point F parallel to segment AH. Point I is the reflection of point B across line Q. Line O is the perpendicular bisector of segment AH. Point Z is the reflection of point I across line O. Find the measure of an... | 0.9 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center Z and circumradius 3. Let Y be the circumcircle of polygon ABCDEFG. Line R is the perpendicular bisector of segment ZG. Circle L is the reflection of circle Y across line R. Point P is the inversion of point D with respect to circle L. Let Q be the midpoi... | 1.0 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center J and circumradius 10. Let Q be the midpoint of segment EF. Let Y be the midpoint of segment QB. Let K be the line through points J and C. Let O be the angle bisector of angle JDE. Let I be the reflection of line O through point C. Point S is the interse... | 31.32 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center W and circumradius 2. Let Z be the reflection of point A across point E. Let L be the line through points F and D. Point X is the reflection of point Z across line L. Let Q be the reflection of point X across point A. Find the measure of angle EZQ, in ra... | 0.52 | MATH |
[
{
"content": "ABCD is a square with center Y and circumradius 8. Let Z be the midpoint of segment BC. Line S passes through points Z and B. Let T be the reflection of point Z across point C. Let E be the reflection of line S through point Y. Let J be the circumcircle of polygon ABCD. Point P is the midpoint of ... | 16.49 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center F and circumradius 1. Let N be the angle bisector of angle AFE. Let Q be the line through point A parallel to line N. Let V be the reflection of line N across line Q. Let Y be the midpoint of segment EF. Point W is the reflection of point Y across point F. ... | 2.49 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center I and circumradius 10. Point R is obtained by rotating point I by angle 5pi/12 about point D. Let W be the circumcircle of polygon ABCDEF. Line G passes through points I and F. Point V is the reflection of point R across line G. Point N is the inversion of p... | 3.96 | MATH |
[
{
"content": "Let ACDEF be a regular 5-gon with center B and circumradius 5. Point Q is the midpoint of segment AC. Let H be the perpendicular bisector of segment DQ. Line M is the reflection of line H across point E. Point J is the reflection of point F across line M. What is the length of segment JC? Express ... | 19.59 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center N and circumradius 3. Let K be the reflection of point F across point A. Line L passes through point A perpendicular to segment KC. Point M is the reflection of point G across line L. Find the distance between points M and D. Express your answer as a decimal ... | 7.74 | MATH |
[
{
"content": "Let ACDEFGHI be a regular octagon with center B and circumradius 7. Let M be the rotation of point H by angle 5pi/6 around point C. Let K be the midpoint of segment CH. Line P is the perpendicular bisector of segment IM. Point L is the reflection of point D across line P. Find the length of segmen... | 12.16 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center Q and circumradius 3. Let W be the angle bisector of angle EAK. Let V be the reflection of line W through point C. Line O passes through point B parallel to line V. Let X be the reflection of line V across line O. Point M is the reflection of point Q acr... | 40.45 | MATH |
[
{
"content": "Let ABCDEFGIJKLM be a regular dodecagon with center H and circumradius 4. Let N be the circumcircle of polygon ABCDEFGIJKLM. Let P be the midpoint of segment ME. Let Q be the angle bisector of angle JEI. Let R be the reflection of line Q through point P. Circle T is the reflection of circle N acro... | 12.74 | MATH |
[
{
"content": "Let ABCDEFHIJK be a regular 10-gon with center G and circumradius 2. Let U be the midpoint of segment FH. Let X be the angle bisector of angle BDU. Point L is the reflection of point K across line X. Let R be the circumcircle of polygon ABCDEFHIJK. Point O is the inversion of point L with respect ... | 4.11 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center S and circumradius 3. Point J is the intersection of segments EB and DG. Let H be the reflection of point F across point G. Let M be the midpoint of segment JH. What is the distance between points M and H? Express your answer as a decimal number rounded to 2 ... | 2.88 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center O and circumradius 8. Let N be the circumcircle of polygon ABCDEFGHI. Let K be the reflection of point D across point G. Point M is the reflection of point B across point K. Point X is the inversion of point M with respect to circle N. What is the distance ... | 7.58 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center R and circumradius 11. Line Y passes through points B and L. Let N be the circumcircle of polygon ABCDEFGHIJKL. Line S passes through point H parallel to line Y. Let P be the reflection of circle N across line S. Let U be the inversion of point J in ... | 23.29 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center P and circumradius 4. Point N is obtained by rotating point P by angle pi/12 about point A. Point G is the midpoint of segment DN. Point T is the reflection of point E across point G. Point I is the reflection of point C across point B. Point M is the refle... | 5.84 | MATH |
[
{
"content": "Let ABCD be a square with center Z and circumradius 11. Let M be the reflection of point A across point C. Point I is the midpoint of segment DM. Point Q is obtained by rotating point M by angle pi/4 about point I. Let N be the rotation of point M by angle 2pi/3 around point Q. Let L be the line t... | 42.37 | MATH |
[
{
"content": "ACDEFG is a regular hexagon with center B and circumradius 3. Point V is the reflection of point A across point C. Let O be the reflection of point E across point F. Point X is the midpoint of segment GO. Point N is the midpoint of segment DV. Find the distance between points N and X. Express your... | 7.94 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center V and circumradius 5. Let P be the line through points A and H. Let Y be the line through point B perpendicular to line P. Point I is the reflection of point B across line P. Let R be the line through point H parallel to line Y. Point L is the reflecti... | 7.07 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center M and circumradius 1. Line Q is the angle bisector of angle AFH. Point O is the reflection of point C across line Q. Point Y is the reflection of point E across segment BO. Find the distance between points M and Y. Express your answer as a decimal numb... | 2.36 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center L and circumradius 4. Let Y be the circumcircle of polygon ABCDEF. Let R be the midpoint of segment LF. Line Q is the angle bisector of angle LRD. Let J be the reflection of point L across point B. Circle W is the reflection of circle Y across line Q. Point ... | 5.08 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center L and circumradius 5. Let Z be the circumcircle of polygon ABCDEFGH. Let V be the midpoint of segment DG. Point X is the inversion of point V with respect to circle Z. Line J is the angle bisector of angle LGE. Point O is the reflection of point F across l... | 13.99 | MATH |
[
{
"content": "ABCDEFGIJKLM is a regular dodecagon with center H and circumradius 6. Point S is the midpoint of segment MK. Point Y is the reflection of point I across point B. Point P is the reflection of point J across segment SA. Find the length of segment PY. Express your answer as a decimal number rounded t... | 22.61 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center K and circumradius 4. Let Y be the midpoint of segment FI. Point N is the reflection of point H across point D. Let M be the line through points Y and K. Let U be the midpoint of segment GH. Point Z is the reflection of point N across line M. Find the... | 14.52 | MATH |
[
{
"content": "Let ABCDEFHIJKLM be a regular dodecagon with center G and circumradius 11. Line O is the angle bisector of angle FGM. Line S passes through point L perpendicular to line O. Point Z is the reflection of point B across line S. Let T be the midpoint of segment CZ. Find the length of segment TK. Expre... | 5.5 | MATH |
[
{
"content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 10. Let P be the perpendicular bisector of segment BA. Line Z passes through point G parallel to line P. Point S is the reflection of point D across line Z. What is the length of segment LS? Express your answer as a decimal number ... | 23.94 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center M and circumradius 4. Line V passes through point A parallel to segment BH. Point L is the reflection of point H across line V. Point Q is the midpoint of segment AG. What is the distance between points Q and L? Express your answer as a decimal number roun... | 3.28 | MATH |
[
{
"content": "ABCDFGHI is a regular octagon with center E and circumradius 6. Let R be the circumcircle of polygon ABCDFGHI. Let M be the reflection of circle R through point I. Let N be the reflection of point H across point A. Point W is the inversion of point N with respect to circle M. Find the length of se... | 9.06 | MATH |
[
{
"content": "Let ABCDEFGIJKLM be a regular dodecagon with center H and circumradius 4. Line W is the perpendicular bisector of segment MB. Line O passes through point C perpendicular to line W. Let Y be the circumcircle of polygon ABCDEFGIJKLM. Let N be the reflection of circle Y across line O. Circle S is the... | 11.31 | MATH |
[
{
"content": "HS = 6. Let ABCDEFGI be a regular octagon with center S and circumradius 1. Let K be the reflection of point D across point E. Let W be the circumcircle of polygon ABCDEFGI. Let Z be the inversion of point K in circle W. Point P is the reflection of point F across segment ZA. Find the distance bet... | 0.15 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center W and circumradius 1. Let M be the midpoint of segment EI. Line Y is the perpendicular bisector of segment IJ. Let V be the line through point I parallel to line Y. Point X is the reflection of point E across line V. What is the measure of angle MIX,... | 0.52 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center W and circumradius 6. Let H be the perpendicular bisector of segment ED. Let T be the reflection of line H through point C. Point P is the reflection of point G across line T. Point J is the midpoint of segment PB. Find the length of segment JD. Express your ... | 16.55 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center T and circumradius 5. Let W be the line through point F parallel to segment BT. Line S passes through point G parallel to segment FJ. Lines S and W intersect at point Q. Find the measure of angle IQE, in radians. Express your answer as a decimal number ro... | 1.26 | MATH |
[
{
"content": "Let UI = 6. Let ABCDE be a regular 5-gon with center I and circumradius 4. Let N be the line through points I and D. Let T be the line through point B perpendicular to line N. Let R be the line through point E perpendicular to line T. Point M is the reflection of point B across line R. Let Z be th... | 0.31 | MATH |
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