messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
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{
"content": "Let ABCDE be a regular 5-gon with center V and circumradius 12. Z is placed 10 units away from E. Let S be the perpendicular bisector of segment BV. Let X be the midpoint of segment BV. Let P be the reflection of point Z across point X. Point G is the reflection of point P across segment DE. Point... | 31.42 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center U and circumradius 10. Line N passes through points A and B. Let Z be the reflection of line N through point C. Let H be the reflection of line Z through point U. Line Y passes through point C perpendicular to line H. Point X is the reflection of point A ac... | 36.18 | MATH |
[
{
"content": "ACDEFGHIJK is a regular 10-gon with center B and circumradius 9. Line O is the angle bisector of angle JGB. Line V is the reflection of line O across point E. Point M is the reflection of point F across line V. Let S be the midpoint of segment HM. Point Q is the reflection of point G across point ... | 33.21 | MATH |
[
{
"content": "ABCEFGHIJK is a regular 10-gon with center D and circumradius 11. Line M passes through points A and I. Let L be the line through point B perpendicular to line M. Line N passes through point G parallel to line L. Point X is the reflection of point H across line N. Find the measure of angle HGX, in... | 0.63 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center Q and circumradius 2. Let Y be the line through points C and Q. Let N be the reflection of point H across point G. Let Z be the line through points N and E. Lines Z and Y intersect at point P. Find the distance between points P and H. Express your answer ... | 10.47 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 12. Let U be the midpoint of segment GH. Let Y be the midpoint of segment HU. Line T is the perpendicular bisector of segment YE. Point I is the reflection of point U across line T. Find the length of segment CI. Express your answer ... | 18.28 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 2. Let I be the perpendicular bisector of segment AB. Line Y passes through point K perpendicular to line I. Line R is the reflection of line Y across point B. Line L is the reflection of line Y across line R. Let J be the line through poi... | 12.17 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Y and circumradius 5. Let Q be the reflection of point Y across point E. Let O be the rotation of point C by angle pi/4 around point B. Point W is the midpoint of segment FD. Let S be the line through point Q parallel to segment OW. Point K is on line S. L... | 20.0 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center Q and circumradius 3. Let P be the midpoint of segment DA. Let Z be the circumcircle of polygon ABCDE. Let Y be the inversion of point P in circle Z. Point L is the midpoint of segment BY. What is the distance between points P and L? Express your answer as a de... | 2.85 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center L and circumradius 7. Let K be the midpoint of segment CB. Point J is the reflection of point F across segment CB. Let P be the midpoint of segment LJ. Point U is the reflection of point K across point F. Find the distance between points U and P. Express you... | 27.78 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center V and circumradius 5. Let O be the perpendicular bisector of segment CH. Let U be the midpoint of segment HE. Line K passes through point D parallel to line O. Point Z is the reflection of point U across line K. Find the length of segment ZG. Express your ... | 15.22 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 3. Let J be the perpendicular bisector of segment HG. Let T be the reflection of point F across point G. Let K be the line through point H perpendicular to line J. Point S is the reflection of point X across line K. Find the measure ... | 0.39 | MATH |
[
{
"content": "Let ABDEFG be a regular hexagon with center C and circumradius 6. Line P passes through points D and A. Line Q passes through points C and E. Line L is the reflection of line P across line Q. Point Y is the reflection of point D across line L. What is the distance between points G and Y? Express y... | 6.0 | MATH |
[
{
"content": "ABCDFG is a regular hexagon with center E and circumradius 5. Let M be the midpoint of segment AB. Let Z be the reflection of point E across point A. Point O is the reflection of point E across segment ZM. What is the distance between points O and Z? Express your answer as a decimal number rounded... | 10.0 | MATH |
[
{
"content": "ABCEFGHIJK is a regular 10-gon with center D and circumradius 8. Line M is the angle bisector of angle GHD. Line Z passes through point G parallel to line M. Let S be the circumcircle of polygon ABCEFGHIJK. Let Y be the reflection of line Z across line M. Point V is the reflection of point G acros... | 19.03 | MATH |
[
{
"content": "ABCD is a square with center F and circumradius 11. Point E is the reflection of point F across point A. Point G is the reflection of point E across point F. Point V is the reflection of point G across segment EB. What is the distance between points C and V? Express your answer as a decimal number... | 35.81 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center V and circumradius 1. Point S is the midpoint of segment EG. Let T be the circumcircle of polygon ABCDEFGHIJ. Let R be the reflection of circle T through point F. Let Q be the inversion of point G in circle R. What is the distance between points Q and S? ... | 0.61 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center L and circumradius 5. Point S is the midpoint of segment BD. Line K passes through points A and S. Let O be the midpoint of segment CB. Let M be the reflection of line K through point O. Point X is the reflection of point B across line M. Find the length of ... | 3.27 | MATH |
[
{
"content": "Let ABCDEFHIJKLM be a regular dodecagon with center G and circumradius 2. Let W be the circumcircle of polygon ABCDEFHIJKLM. Line N is the angle bisector of angle EFG. Point Q is the reflection of point E across line N. Point S is the inversion of point Q with respect to circle W. Find the distanc... | 2.61 | MATH |
[
{
"content": "Let ACDEFG be a regular hexagon with center B and circumradius 2. Let S be the circumcircle of polygon ACDEFG. Let O be the midpoint of segment GE. Point Y is the midpoint of segment BD. Let P be the inversion of point Y in circle S. Find the length of segment PO. Express your answer as a decimal ... | 4.58 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Z and circumradius 9. Point R is the reflection of point E across point D. Let I be the circumcircle of polygon ABCDE. Line X is the perpendicular bisector of segment RC. Circle Y is the reflection of circle I across line X. Point O is the inversion of poin... | 12.82 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center G and circumradius 1. Let L be the line through points E and D. Let R be the reflection of line L through point G. Point K is the reflection of point C across point G. Point Z is the reflection of point C across line R. What is the length of segment ZK? Exp... | 2.5 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 7. Line P is the perpendicular bisector of segment BA. Point R is the reflection of point F across segment BA. Point U is the reflection of point R across line P. What is the measure of angle RUD, in radians? Express your answer as a decimal ... | 1.26 | MATH |
[
{
"content": "ABCDEFGHIJKM is a regular dodecagon with center L and circumradius 4. Let R be the line through points D and C. Let O be the reflection of line R through point A. Let U be the line through point J perpendicular to line O. Point T is the reflection of point G across line U. Find the distance betwee... | 9.58 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center S and circumradius 11. Line R is the perpendicular bisector of segment AS. Let V be the circumcircle of polygon ABCDEFG. Circle L is the reflection of circle V across line R. Let H be the reflection of circle L through point B. Point Z is the inversion of poi... | 16.78 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Q and circumradius 1. Let X be the midpoint of segment QG. Line O is the angle bisector of angle CFX. Let M be the reflection of line O through point X. Point U is the reflection of point Q across line M. Find the length of segment AU. Express your ans... | 1.03 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 3. Point W is obtained by rotating point F by angle pi/4 about point B. Let L be the midpoint of segment CB. Let T be the line through points G and L. Let Q be the rotation of point B by angle pi/4 around point F. Point N is the midp... | 2.18 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center W and circumradius 5. Point T is the reflection of point W across segment BA. Point M is the midpoint of segment BA. Line Z passes through points D and M. Point P is the reflection of point B across line Z. What is the distance between points P and T? Ex... | 6.04 | MATH |
[
{
"content": "Let ACDEFG be a regular hexagon with center B and circumradius 5. Line W passes through points B and E. Let Z be the angle bisector of angle DEA. Point N is the midpoint of segment BD. Let J be the reflection of line W through point D. Line L is the reflection of line J across line Z. Point U is t... | 12.5 | MATH |
[
{
"content": "Let ABCDEFHIJKL be a regular 11-gon with center G and circumradius 5. Let U be the reflection of point J across point G. Let V be the angle bisector of angle UJH. Let N be the reflection of line V through point U. Point R is the reflection of point F across line N. What is the distance between poi... | 23.52 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Y and circumradius 7. Let S be the rotation of point J by angle pi around point A. Let X be the midpoint of segment KA. Let Q be the reflection of point S across point I. Point Z is the midpoint of segment FX. Find the length of segment ZQ. Expre... | 28.26 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center W and circumradius 4. Let Q be the rotation of point I by angle 5pi/12 around point K. Let S be the line through points J and A. Let N be the reflection of point W across point A. Let T be the line through point N parallel to line S. Point U is the r... | 11.96 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center Q and circumradius 2. Point Y is the reflection of point F across point G. Point T is the midpoint of segment YE. Let U be the midpoint of segment GT. Point M is the reflection of point B across segment TU. Find the length of segment MB. Express your ... | 4.7 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 11. Line W is the angle bisector of angle AHB. Let J be the line through point G parallel to line W. Segment AE and line J intersect at point Z. Point N is the reflection of point D across line W. Let Y be the reflection of point N a... | 12.74 | MATH |
[
{
"content": "ABCDFGHI is a regular octagon with center E and circumradius 2. Let L be the angle bisector of angle CFE. Line T is the reflection of line L across point C. Let Z be the reflection of line L across line T. Let S be the reflection of point B across point C. Point N is the reflection of point E acro... | 7.27 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Q and circumradius 6. Let H be the perpendicular bisector of segment DC. Let V be the reflection of line H through point C. Point O is the reflection of point E across line V. Point J is the reflection of point O across point D. What is the length of segment... | 21.63 | MATH |
[
{
"content": "Let ABDE be a square with center C and circumradius 6. Let L be the reflection of point D across point B. Point M is the reflection of point C across point E. Point T is the midpoint of segment LM. What is the distance between points L and T? Express your answer as a decimal number rounded to 2 de... | 12.37 | MATH |
[
{
"content": "ABCDFG is a regular hexagon with center E and circumradius 12. Let R be the rotation of point C by angle 5pi/12 around point B. Let O be the line through points D and F. Point J is the reflection of point C across line O. Line P is the angle bisector of angle JCE. Point V is the reflection of poin... | 20.08 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center G and circumradius 9. Let I be the line through points C and D. Point R is the midpoint of segment FA. Point T is the reflection of point G across line I. Let Q be the midpoint of segment TR. What is the length of segment CQ? Express your answer as a decimal... | 5.95 | MATH |
[
{
"content": "Let ABDEFGHI be a regular octagon with center C and circumradius 6. Point X is the midpoint of segment GD. Line Y is the perpendicular bisector of segment IC. Line J passes through point D parallel to line Y. Line M passes through points D and B. Line T passes through point C parallel to line M. L... | 1.96 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 5. Point Z is obtained by rotating point A by angle pi/6 about point F. Point V is the reflection of point N across segment FZ. Point T is the intersection of segments VG and FZ. Find the length of segment TC. Express your answer as ... | 5.15 | MATH |
[
{
"content": "Let ACDE be a square with center B and circumradius 1. Line K is the perpendicular bisector of segment EC. Point U is the midpoint of segment CD. Let H be the line through point D perpendicular to line K. Let P be the reflection of point A across point E. Point J is the reflection of point U acros... | 2.55 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center P and circumradius 3. Line Z passes through points H and C. Let S be the midpoint of segment BG. Point Y is the reflection of point S across line Z. Point U is the midpoint of segment YE. What is the distance between points U and Y? Express your answer... | 2.34 | MATH |
[
{
"content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 7. Let S be the perpendicular bisector of segment EI. Line T passes through points L and I. Let W be the reflection of line T across line S. Lines W and T intersect at point N. Find the measure of angle HDN, in radians. Express... | 2.62 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center W and circumradius 7. Let K be the line through points B and E. Point S is the reflection of point A across line K. Point N is the midpoint of segment SW. Point T is the midpoint of segment DN. What is the distance between points H and T? Express your... | 12.37 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Z and circumradius 5. Point R is the midpoint of segment AZ. Let O be the circumcircle of polygon ABCDE. Point W is the midpoint of segment DR. Point S is the midpoint of segment DW. Circle L is the reflection of circle O across point S. Let X be the invers... | 6.89 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center X and circumradius 8. Point P is obtained by rotating point X by angle pi/2 about point D. Point M is the midpoint of segment XE. Point Y is the reflection of point P across point M. Point T is the reflection of point D across segment MY. What is the length ... | 8.0 | MATH |
[
{
"content": "Let ABCDFGHIJKLM be a regular dodecagon with center E and circumradius 1. Line Q is the perpendicular bisector of segment BI. Let X be the reflection of line Q through point J. Let P be the reflection of point E across point D. Let W be the reflection of point P across point J. Point Z is the refl... | 4.2 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Q and circumradius 3. Let Z be the midpoint of segment DC. Let T be the perpendicular bisector of segment ZE. Point J is on line T. Point G is the reflection of point D across segment JE. What is the length of segment GE? Express your answer as a decimal num... | 3.0 | MATH |
[
{
"content": "MI = 3. ABCDEFGHJKLN is a regular dodecagon with center I and circumradius 1. Line O is the angle bisector of angle BCH. Line P passes through points E and J. Line V is the reflection of line P across line O. Point S is the reflection of point L across line V. Point Y is the midpoint of segment SG... | 1.87 | MATH |
[
{
"content": "ABCDEGHIJ is a regular 9-gon with center F and circumradius 3. Let Z be the perpendicular bisector of segment AG. Point Q lies on line Z at distance 10 from point G. Let O be the reflection of line Z through point H. Line W is the reflection of line O across point B. Let R be the reflection of lin... | 34.37 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 7. Line H passes through points B and D. Let V be the reflection of line H through point F. Point L is the reflection of point A across line H. Point R is the reflection of point L across point D. Let J be the reflection of point F across poi... | 31.3 | MATH |
[
{
"content": "Let ABCDFG be a regular hexagon with center E and circumradius 8. Let M be the reflection of point A across point C. Point Y is the reflection of point G across segment MA. Let W be the reflection of point M across point A. Find the distance between points Y and W. Express your answer as a decimal... | 28.84 | MATH |
[
{
"content": "Let ABCD be a square with center Y and circumradius 10. Point T is the midpoint of segment BY. Point E is the midpoint of segment CD. Let N be the perpendicular bisector of segment EY. Line O passes through point T perpendicular to line N. Point Z is the reflection of point A across line O. Let U ... | 15.81 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center N and circumradius 6. Let Z be the line through points D and C. Let M be the reflection of line Z through point F. Point X is the reflection of point F across line M. Let W be the midpoint of segment DN. What is the length of segment WX? Express your answer ... | 28.62 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center L and circumradius 12. Point T is the midpoint of segment AI. Point X is the reflection of point C across segment TH. What is the distance between points D and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer i... | 38.24 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Y and circumradius 2. Let U be the rotation of point C by angle pi around point D. Point Z is the reflection of point A across point D. Let W be the perpendicular bisector of segment ZY. Line X is the reflection of line W across point C. Line Q is the re... | 15.1 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center W and circumradius 9. Point X is the reflection of point A across point B. Line N passes through points A and W. Let Y be the line through points X and E. Line S is the reflection of line N across line Y. Point M is the intersection of lines S and N. Let... | 14.31 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center Q and circumradius 11. Let P be the reflection of point A across point E. Let M be the circumcircle of polygon ABCDE. Let U be the angle bisector of angle QPD. Let K be the reflection of circle M across line U. Let W be the inversion of point A in circle K. Fin... | 7.83 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center V and circumradius 1. Line O passes through points B and E. Let H be the angle bisector of angle CDA. Let J be the reflection of line H across line O. Line T passes through point C perpendicular to line J. Point U is the reflection of point D across line T.... | 1.54 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center Q and circumradius 6. Line N is the perpendicular bisector of segment HF. Let O be the reflection of line N through point H. Point Z is the reflection of point A across line O. What is the length of segment ZH? Express your answer as a decimal number roun... | 12.0 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center V and circumradius 7. Let O be the circumcircle of polygon ABCDE. Circle N is the reflection of circle O across point D. Let P be the line through points V and D. Let Y be the inversion of point E in circle N. Let S be the perpendicular bisector of segment ... | 20.2 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center I and circumradius 9. Point M is the midpoint of segment GI. Let S be the circumcircle of polygon ABCDEFG. Let T be the angle bisector of angle IGE. Circle W is the reflection of circle S across line T. Let P be the reflection of circle W through point E. Poi... | 17.22 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center K and circumradius 9. Line J passes through points A and C. Line U is the angle bisector of angle ACD. Line W passes through point F parallel to line U. Lines W and J intersect at point T. What is the measure of angle CTB, in radians? Express your answer... | 1.83 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center M and circumradius 9. Line R is the perpendicular bisector of segment DC. Let Y be the reflection of point E across point B. Let Z be the line through point C perpendicular to line R. Point V is the midpoint of segment YC. Point T is the reflection of po... | 22.5 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center Z and circumradius 10. Line M passes through points C and A. Let Q be the line through point D perpendicular to segment GA. Point I is the reflection of point Z across line M. Line X is the reflection of line M across line Q. Line H passes through points ... | 9.19 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center N and circumradius 10. Let J be the midpoint of segment ND. Let R be the perpendicular bisector of segment NB. Point I is the reflection of point J across line R. Point V is the midpoint of segment BI. What is the length of segment IV? Express your answer as a ... | 2.5 | MATH |
[
{
"content": "Let ABDEFGHIJ be a regular 9-gon with center C and circumradius 9. Point Z is the reflection of point F across point C. Line T passes through points E and A. Point Q is the reflection of point Z across line T. Let Y be the line through points A and Z. Point K is the reflection of point B across li... | 3.13 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center U and circumradius 5. Let O be the reflection of point F across point J. Let M be the midpoint of segment IK. Let W be the midpoint of segment MG. What is the distance between points W and O? Express your answer as a decimal number rounded to 2 d... | 12.39 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center V and circumradius 10. Let L be the line through points A and C. Point O is the reflection of point E across line L. Line W passes through points D and C. Point R is the reflection of point F across line W. What is the distance between points R and O... | 17.29 | MATH |
[
{
"content": "ABCDEFGHJ is a regular 9-gon with center I and circumradius 2. Let N be the rotation of point F by angle 2pi/3 around point B. Point L is the reflection of point N across point E. Let U be the midpoint of segment JI. Point Y is the midpoint of segment AU. What is the distance between points L and ... | 10.36 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center U and circumradius 4. Let Z be the circumcircle of polygon ABCDEFGHIJKL. Let T be the reflection of point A across point I. Circle X is the reflection of circle Z across point L. Point Y is the inversion of point B with respect to circle X. What ... | 14.63 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Y and circumradius 7. Point J is the midpoint of segment AF. Point U is obtained by rotating point C by angle 7pi/12 about point J. Line Z passes through points U and C. Line G passes through point B parallel to line Z. Point M is the intersection of lin... | 8.65 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center P and circumradius 7. Point J is the reflection of point D across point G. Let V be the line through point I perpendicular to segment CB. Let N be the reflection of line V through point J. Point U is the reflection of point G across line N. Find the dis... | 18.29 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center W and circumradius 8. Point P is the midpoint of segment JH. Let V be the reflection of point C across point P. Point K is the midpoint of segment JB. What is the distance between points V and K? Express your answer as a decimal number rounded to 2 de... | 20.52 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center I and circumradius 7. Let L be the circumcircle of polygon ABCDEFG. Circle N is the reflection of circle L across point F. Point Y is the inversion of point A with respect to circle N. Let V be the perpendicular bisector of segment IC. Let K be the line t... | 4.76 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center N and circumradius 6. Point Z is the midpoint of segment DA. Point L is the midpoint of segment ZJ. Point O is the reflection of point D across point L. Find the distance between points I and O. Express your answer as a decimal number rounded to 2 decimal... | 6.96 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center U and circumradius 8. Let Y be the line through points H and K. Line Q passes through points C and B. Line V is the reflection of line Y across point J. Point S is the intersection of lines V and Q. What is the distance between points S and B? Express yo... | 17.78 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 9. Let I be the circumcircle of polygon ABCDEF. Let N be the midpoint of segment BF. Point P is the reflection of point N across point E. Point Z is the inversion of point P with respect to circle I. Find the length of segment FZ. Express ... | 8.56 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center O and circumradius 1. Point J is the midpoint of segment FE. Point W is the reflection of point C across segment DB. Point S is the midpoint of segment WF. Point Y is the reflection of point J across point O. What is the distance between points S and Y... | 1.31 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center T and circumradius 2. Let N be the line through points T and G. Line Y is the perpendicular bisector of segment TF. Line U is the reflection of line Y across line N. Point K is the reflection of point A across line U. Find the length of segment KC. Express... | 2.0 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 5. Line X passes through points B and F. Let G be the perpendicular bisector of segment OD. Point M is the reflection of point D across line X. Let R be the angle bisector of angle ABM. Line J is the reflection of line G across line R. Lin... | 11.97 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center P and circumradius 12. Let Y be the perpendicular bisector of segment GB. Line L is the reflection of line Y across point B. Line R passes through point G perpendicular to line L. Point Z is on line R. Point N is the reflection of point Z across point... | 1.89 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center U and circumradius 12. Point Y is obtained by rotating point I by angle pi/2 about point A. Point V is the midpoint of segment EI. Let K be the line through point V parallel to segment IA. Line J passes through point H perpendicular to line K. Point R i... | 33.43 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Y and circumradius 10. Line X is the angle bisector of angle AHJ. Point M is the reflection of point G across line X. Point Z is the midpoint of segment CB. Point P is the reflection of point M across segment LC. What is the distance between poin... | 22.08 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 3. Point T is obtained by rotating point C by angle 2pi/3 about point A. Let W be the line through point H parallel to segment NF. Let Y be the line through point T perpendicular to line W. Point S is the reflection of point A across... | 5.64 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center M and circumradius 1. Line O is the perpendicular bisector of segment GD. Point W is the midpoint of segment FM. Let P be the midpoint of segment WG. Let Q be the line through point P perpendicular to line O. Point X is the reflection of point B acro... | 1.63 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center L and circumradius 5. Let R be the circumcircle of polygon ABCDEFGHIJ. Line Z is the perpendicular bisector of segment CL. Point Q is the midpoint of segment BD. Let U be the reflection of circle R across line Z. Let W be the inversion of point Q in circl... | 26.18 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Z and circumradius 1. Point V is the reflection of point A across point L. Point Q is the reflection of point C across point G. Let N be the angle bisector of angle ZKJ. Line O passes through point H parallel to line N. Let R be the reflection of... | 3.41 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center M and circumradius 12. Line H passes through point A perpendicular to segment DM. Let J be the line through point D parallel to line H. Point Y is the reflection of point M across line J. Let L be the reflection of point M across point Y. What is the dis... | 54.99 | MATH |
[
{
"content": "Let ABCD be a square with center K and circumradius 4. Line W is the angle bisector of angle BAC. Let M be the midpoint of segment KD. Line U is the reflection of line W across point B. Point Z is the reflection of point D across line U. Point O is the reflection of point D across point Z. Point P... | 36.44 | MATH |
[
{
"content": "ABCDEGHIJK is a regular 10-gon with center F and circumradius 6. Line S is the angle bisector of angle IGB. Let O be the reflection of line S through point J. Let V be the reflection of line O through point E. Line X is the reflection of line V across point H. Point M is the reflection of point D ... | 42.54 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center H and circumradius 1. Let L be the reflection of point E across point A. Point Q is the midpoint of segment LC. Let U be the reflection of point L across point E. Point X is the midpoint of segment QL. What is the distance between points X and U? Express yo... | 4.29 | MATH |
[
{
"content": "Let ABCEFGHI be a regular octagon with center D and circumradius 4. Point V is the midpoint of segment EA. Line J is the angle bisector of angle FGV. Let N be the line through point F parallel to line J. Line X is the reflection of line J across line N. Point P is the midpoint of segment BF. Point... | 14.24 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center L and circumradius 7. Let J be the reflection of point A across point E. Let M be the circumcircle of polygon ABCDEFGH. Circle K is the reflection of circle M across point G. Let X be the inversion of point B in circle K. What is the length of segment JX? ... | 24.54 | MATH |
[
{
"content": "ABCDEFGHJK is a regular 10-gon with center I and circumradius 8. Let R be the angle bisector of angle GKC. Let Q be the line through point F parallel to line R. Let M be the reflection of line Q across line R. Point Y is the reflection of point C across line M. Find the distance between points J a... | 11.06 | MATH |
[
{
"content": "Let ABCDEFGHJKLM be a regular dodecagon with center I and circumradius 1. Let Z be the line through points G and F. Line Q passes through point I parallel to line Z. Line W is the reflection of line Z across line Q. Point N is the reflection of point G across line W. Find the distance between poin... | 3.63 | MATH |
[
{
"content": "ABDEFGHIJKLM is a regular dodecagon with center C and circumradius 11. Let N be the reflection of point D across point K. Point P is the midpoint of segment NG. Let T be the midpoint of segment LJ. Find the distance between points P and T. Express your answer as a decimal number rounded to 2 decim... | 8.28 | MATH |
[
{
"content": "Let ABCDFGHIJK be a regular 10-gon with center E and circumradius 8. Line S passes through points H and G. Line Y passes through point J parallel to line S. Point R is the reflection of point H across point A. Let X be the midpoint of segment GR. Line Y and segment HK intersect at point L. Find th... | 9.07 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Y and circumradius 11. Line Z is the angle bisector of angle FEA. Point S is the reflection of point D across line Z. Point U is the reflection of point G across point S. Point L is the midpoint of segment HC. Find the length of segment LU. Express your an... | 37.88 | MATH |
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