messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
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[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center S and circumradius 8. Let R be the line through points H and C. Point P is the reflection of point F across line R. Let V be the angle bisector of angle EHI. Point M is the reflection of point B across line V. What is the measure of angle MPA, in... | 0.52 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center H and circumradius 6. Point N is obtained by rotating point B by angle 5pi/6 about point D. Let I be the circumcircle of polygon ABCDEF. Let Q be the reflection of circle I through point D. Let P be the inversion of point N in circle Q. Let Y be the line... | 17.59 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center Z and circumradius 4. Line W is the perpendicular bisector of segment BA. Line R is the perpendicular bisector of segment JB. Line M is the reflection of line W across line R. Point L is the intersection of segment KG and line M. What is the length of se... | 6.29 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 6. Let W be the midpoint of segment FX. Let Q be the midpoint of segment EW. Let K be the line through points C and Q. Point L is the reflection of point B across line K. What is the distance between points B and L? Express your answ... | 9.11 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center W and circumradius 3. Let Q be the reflection of point W across point C. Let G be the rotation of point E by angle 7pi/12 around point W. Let R be the rotation of point C by angle pi/4 around point D. Let U be the vector from point F to point D. Let Z be... | 3.04 | MATH |
[
{
"content": "BH = 11. Let ACDEFG be a regular hexagon with center H and circumradius 12. Let K be the rotation of point C by angle pi around point F. Let W be the reflection of point G across point C. Point M is the reflection of point K across point D. Let N be the midpoint of segment WC. What is the distance... | 31.18 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Y and circumradius 5. Line W is the angle bisector of angle GIF. Let M be the circumcircle of polygon ABCDEFGHIJKL. Circle T is the reflection of circle M across line W. Let O be the inversion of point K in circle T. Find the length of segment OK... | 7.39 | MATH |
[
{
"content": "Let ABCDEFGHIJL be a regular 11-gon with center K and circumradius 10. Line N is the perpendicular bisector of segment KB. Point W is the reflection of point D across line N. Line R is the angle bisector of angle LWD. Line Z is the reflection of line N across line R. Let U be the reflection of lin... | 19.64 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center S and circumradius 12. Let P be the line through points C and F. Point N is the reflection of point H across point J. Line U is the perpendicular bisector of segment HE. Let Y be the reflection of line P across line U. Point R is the reflection of po... | 22.69 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center V and circumradius 7. Let U be the line through points E and D. Let O be the reflection of line U through point A. Line P is the reflection of line U across line O. Point R is the reflection of point B across point F. Point S is the reflection of point D... | 99.24 | MATH |
[
{
"content": "Let ABDEF be a regular 5-gon with center C and circumradius 1. Point L is the reflection of point A across point C. Point W is the reflection of point A across point L. Point Q is the midpoint of segment WC. Let K be the midpoint of segment WB. What is the distance between points K and Q? Express ... | 0.5 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center M and circumradius 7. Line N is the angle bisector of angle BCF. Let X be the reflection of line N through point E. Let R be the rotation of point M by angle 5pi/12 around point C. Point Z is the reflection of point R across line X. Point O is th... | 29.65 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Y and circumradius 6. Let G be the line through points E and F. Point Q is the reflection of point D across line G. Let M be the midpoint of segment QE. Let Z be the reflection of point Y across point M. What is the distance between points Z and D? Express y... | 15.87 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center N and circumradius 9. Let Y be the perpendicular bisector of segment CB. Line J is the reflection of line Y across point A. Point I is the reflection of point C across line J. Point Z is the midpoint of segment DF. Point T is the reflection of point I ac... | 56.2 | MATH |
[
{
"content": "ABCDEFGI is a regular octagon with center H and circumradius 8. Let Q be the perpendicular bisector of segment CB. Let X be the angle bisector of angle FGD. Line P is the reflection of line Q across line X. Let V be the line through point G perpendicular to line P. Let M be the reflection of line ... | 11.55 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center W and circumradius 6. Line T is the perpendicular bisector of segment EJ. Let S be the line through points C and E. Let M be the reflection of line T across line S. Point V is the intersection of lines S and M. What is the distance between points C and V?... | 3.15 | MATH |
[
{
"content": "Let ABCD be a square with center O and circumradius 8. Let W be the rotation of point A by angle pi/6 around point D. Let X be the line through points O and A. Point P is the reflection of point W across line X. Point Q is the reflection of point C across segment AP. Find the distance between poin... | 21.86 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center K and circumradius 3. Let V be the angle bisector of angle KAC. Point L is the reflection of point K across line V. Let P be the midpoint of segment LA. What is the distance between points B and P? Express your answer as a decimal number rounded to 2 decim... | 1.08 | MATH |
[
{
"content": "ABCDEFHIJK is a regular 10-gon with center G and circumradius 2. Point N is obtained by rotating point K by angle 2pi/3 about point D. Point P is obtained by rotating point H by angle 5pi/12 about point K. Let T be the perpendicular bisector of segment GA. Line L passes through point P parallel to... | 6.35 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center P and circumradius 11. Point V is the reflection of point A across segment DB. Let M be the midpoint of segment KI. Let W be the reflection of point G across point V. What is the length of segment MW? Express your answer as a decimal number round... | 47.29 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center I and circumradius 9. Let P be the rotation of point E by angle pi/3 around point I. Point J is the midpoint of segment AB. Point Z is the midpoint of segment BP. Let X be the reflection of point Z across point A. Point G is the reflection of point X across seg... | 10.15 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center M and circumradius 1. Let O be the perpendicular bisector of segment DM. Line H passes through point D perpendicular to line O. Point N is the reflection of point C across segment ED. Line Q passes through point D perpendicular to line H. Let Z be the line ... | 1.84 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center I and circumradius 8. Point O is obtained by rotating point D by angle pi/6 about point F. Line P is the angle bisector of angle OBC. Point Y is the reflection of point O across line P. Point W is the reflection of point Y across segment OD. What is the ... | 10.28 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 8. Line V passes through points H and C. Point J lies on line V. Line Z passes through points E and J. Point I is the reflection of point A across line Z. What is the distance between points E and I? Express your answer as a decimal ... | 16.0 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center P and circumradius 2. Line R is the angle bisector of angle PDH. Point W is the reflection of point G across point F. Point Z is the reflection of point B across line R. Point V is the reflection of point Z across point W. What is the distance be... | 0.54 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Y and circumradius 9. Let M be the line through point C perpendicular to segment FB. Let I be the reflection of line M through point F. Point U is the reflection of point E across line I. What is the measure of angle HEU, in radians? Express your answer as... | 1.96 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center P and circumradius 5. Let O be the midpoint of segment EP. Let I be the reflection of point O across point P. Point H is the midpoint of segment PC. What is the distance between points I and H? Express your answer as a decimal number rounded to 2 decimal pl... | 1.55 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center S and circumradius 4. Let U be the midpoint of segment JC. Point L is obtained by rotating point F by angle 3pi/4 about point H. Let Q be the perpendicular bisector of segment UF. Point Y is the reflection of point C across line Q. Line N is the angle... | 14.75 | MATH |
[
{
"content": "Let ABCEFGHI be a regular octagon with center D and circumradius 5. Point U is the reflection of point I across point H. Let X be the angle bisector of angle EDA. Let O be the reflection of line X through point U. Let M be the line through point U parallel to line O. Line M and segment AC intersec... | 4.23 | MATH |
[
{
"content": "Let ABCDEGHIJ be a regular 9-gon with center F and circumradius 8. Point R is the reflection of point E across segment JB. Let Q be the line through point I perpendicular to segment JB. Point O is the reflection of point F across line Q. What is the length of segment OR? Express your answer as a d... | 27.07 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center V and circumradius 3. Let M be the midpoint of segment KH. Let Z be the line through points A and F. Point U lies on line Z. Find the measure of angle UFM, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresen... | 0.79 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center T and circumradius 6. Let Y be the circumcircle of polygon ABCDE. Let N be the angle bisector of angle DBE. Let M be the reflection of circle Y through point D. Line Z passes through point B perpendicular to line N. Let X be the inversion of point C in circle M... | 16.81 | MATH |
[
{
"content": "ABCD is a square with center T and circumradius 1. Point O is the midpoint of segment BT. Let W be the perpendicular bisector of segment CD. Point Y is the reflection of point O across line W. What is the length of segment YO? Express your answer as a decimal number rounded to 2 decimal places.\n\... | 0.71 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center Y and circumradius 2. Point O is the reflection of point H across point A. Point V is the midpoint of segment OF. Point Z is the midpoint of segment VG. What is the length of segment ZO? Express your answer as a decimal number rounded to 2 decimal pla... | 5.18 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center M and circumradius 12. Let S be the vector from point J to point I. Point L is the reflection of point H across point A. Point U is the translation of point G by vector S. Let K be the line through points U and M. Line R passes through point H perpend... | 30.6 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center L and circumradius 5. Point Q is the reflection of point J across point D. Line T is the angle bisector of angle BQI. Line K passes through point E perpendicular to line T. Point M is the reflection of point A across line K. What is the length of segm... | 9.93 | MATH |
[
{
"content": "ABCD is a square with center T and circumradius 11. Let J be the reflection of point A across point D. Let V be the circumcircle of polygon ABCD. Let S be the inversion of point J in circle V. Let R be the reflection of point S across point C. Let X be the midpoint of segment CJ. Let L be the inve... | 13.34 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center P and circumradius 5. Point Y is on segment GE. Point N is the reflection of point H across segment CY. Find the length of segment NC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\b... | 9.66 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center U and circumradius 7. Point X is the reflection of point D across point F. Line Q is the angle bisector of angle FEB. Line W passes through points X and B. Point I is on line W. Line Z is the reflection of line Q across point I. Point P is the reflection of p... | 0.45 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center V and circumradius 6. Line Q passes through points F and B. Let M be the line through point C parallel to segment VE. Lines Q and M intersect at point H. What is the measure of angle ADH, in radians? Express your answer as a decimal number rounded to 2 d... | 1.05 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center R and circumradius 5. Let W be the perpendicular bisector of segment AI. Let V be the line through point F perpendicular to line W. Line M is the reflection of line V across point H. Point T is the reflection of point E across line M. What is the distance... | 23.5 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center U and circumradius 6. Let I be the reflection of point B across point U. Let M be the midpoint of segment UB. Point L is the midpoint of segment EU. Let Y be the reflection of point L across point I. What is the distance between points M and Y? Express your... | 12.7 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center O and circumradius 6. Let W be the angle bisector of angle EHB. Line X passes through point E parallel to line W. Let Z be the line through point D parallel to segment BC. Lines X and Z intersect at point T. Find the measure of angle BDT, in radians. E... | 2.75 | MATH |
[
{
"content": "Let ABCDEFGHIJLM be a regular dodecagon with center K and circumradius 7. Let Q be the angle bisector of angle EAG. Line S is the perpendicular bisector of segment KC. Point T is the reflection of point M across line S. Point W is the reflection of point T across line Q. What is the measure of ang... | 0.52 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center K and circumradius 8. Line L passes through points A and C. Let G be the circumcircle of polygon ABCDE. Let W be the rotation of point B by angle 5pi/12 around point E. Point Y is the reflection of point W across line L. Point J is the reflection of point E acr... | 9.54 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center P and circumradius 8. Let S be the midpoint of segment PE. Let J be the midpoint of segment EC. Point I is the midpoint of segment SH. Find the length of segment JI. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer... | 8.36 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center O and circumradius 4. Let R be the perpendicular bisector of segment AB. Let J be the angle bisector of angle ADH. Line T passes through point B parallel to line J. Point L is the reflection of point C across line J. Let X be the reflection of line T a... | 31.5 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center J and circumradius 8. Let F be the rotation of point E by angle pi/3 around point C. Point O is obtained by rotating point F by angle 7pi/12 about point J. Line V is the angle bisector of angle OAF. Let N be the line through point O perpendicular to line V.... | 21.56 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center G and circumradius 3. Let M be the rotation of point G by angle 5pi/12 around point D. Let Q be the rotation of point E by angle 7pi/12 around point A. Point Z is the reflection of point A across point D. Line P is the perpendicular bisector of segment QD. L... | 11.76 | MATH |
[
{
"content": "Let ABCDEGHI be a regular octagon with center F and circumradius 6. Line Y passes through points H and B. Point N is the reflection of point F across point A. Line O is the reflection of line Y across point N. Point K is the reflection of point D across line O. What is the length of segment NK? Ex... | 34.29 | MATH |
[
{
"content": "Let ABDEFGHI be a regular octagon with center C and circumradius 4. Let J be the reflection of point D across point B. Let W be the reflection of point E across point F. Let R be the midpoint of segment JH. Let S be the reflection of point R across point W. What is the length of segment RS? Expres... | 16.34 | MATH |
[
{
"content": "ABCDEGHIJKLM is a regular dodecagon with center F and circumradius 8. Point Y is the reflection of point A across point I. Let P be the circumcircle of polygon ABCDEGHIJKLM. Point R is the midpoint of segment GY. Let Z be the inversion of point R in circle P. What is the distance between points Z ... | 6.33 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center S and circumradius 11. Point V is the reflection of point H across point G. Line U passes through points I and C. Line O is the perpendicular bisector of segment HI. Line M is the reflection of line O across point G. Point X is the intersection of lines ... | 130.53 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center Q and circumradius 5. Let R be the angle bisector of angle HAG. Let X be the midpoint of segment IE. Point S is the reflection of point X across point E. Point U is the reflection of point H across line R. What is the length of segment SU? Express your an... | 10.17 | MATH |
[
{
"content": "Let ABCD be a square with center Y and circumradius 3. Let T be the perpendicular bisector of segment CB. Let W be the reflection of line T through point A. Point V is the midpoint of segment YC. Let F be the midpoint of segment DA. Point Z is the reflection of point F across line W. What is the l... | 10.06 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Y and circumradius 6. Line Q is the angle bisector of angle CJY. Let W be the reflection of point H across point F. Point X is the reflection of point E across line Q. Point T is the reflection of point X across point W. Point M is the reflection... | 13.41 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center H and circumradius 6. Let O be the reflection of point G across point B. Point R is the midpoint of segment GD. Let Y be the perpendicular bisector of segment RO. Point X is the reflection of point G across line Y. Find the length of segment EX. Express your ... | 22.79 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center M and circumradius 11. Let S be the angle bisector of angle DMA. Let V be the perpendicular bisector of segment EA. Let I be the reflection of line V across line S. Line Z passes through point D parallel to line S. Lines I and Z intersect at point L. What is th... | 0.63 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center X and circumradius 6. Point N is the reflection of point B across point J. Let M be the line through point X perpendicular to segment XN. Let V be the reflection of line M through point C. Let L be the reflection of line V across line M. Line T is the ref... | 18.56 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center L and circumradius 6. Let W be the angle bisector of angle JEI. Let O be the perpendicular bisector of segment JC. Let M be the reflection of line O through point H. Point Q is the reflection of point D across line M. Point X is the reflection of poin... | 21.28 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center G and circumradius 5. Line H passes through points B and A. Point W is on line H. Let U be the midpoint of segment BE. Find the measure of angle WBU, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in L... | 0.63 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center T and circumradius 6. Line I passes through points T and E. Line V is the reflection of line I across point D. Point U is obtained by rotating point D by angle pi about point E. Let X be the midpoint of segment TD. Let G be the line through points E and ... | 26.15 | MATH |
[
{
"content": "BCDEFGHIJ is a regular 9-gon with center A and circumradius 2. Let Y be the reflection of point G across point J. Let P be the perpendicular bisector of segment DY. Let Z be the reflection of line P through point B. Point R is the intersection of segment DY and line Z. What is the distance between... | 3.81 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center O and circumradius 7. Let I be the circumcircle of polygon ABCDEFG. Let T be the midpoint of segment ED. Point J is the midpoint of segment CB. Circle H is the reflection of circle I across point C. Point X is the inversion of point T with respect to circ... | 6.71 | MATH |
[
{
"content": "ABCDEG is a regular hexagon with center F and circumradius 11. Let S be the reflection of point A across point G. Line P passes through points B and E. Let R be the midpoint of segment FS. Line M passes through point E perpendicular to line P. Let U be the reflection of line M through point F. Lin... | 39.66 | MATH |
[
{
"content": "ABCDEFGIJK is a regular 10-gon with center H and circumradius 5. Point W is the reflection of point H across segment FB. Let Y be the reflection of point W across point B. Let R be the midpoint of segment FB. Point V is the midpoint of segment RY. Find the distance between points G and V. Express ... | 9.79 | MATH |
[
{
"content": "Let ABCDEFHIJK be a regular 10-gon with center G and circumradius 3. Let P be the line through points J and E. Point L is the reflection of point E across point K. Line T passes through point L parallel to line P. Let W be the reflection of point A across point F. Segment AB and line T intersect a... | 0.63 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center P and circumradius 1. Let R be the midpoint of segment CA. Let W be the line through points D and F. Line S is the reflection of line W across point B. Point M is the reflection of point R across line S. Find the distance between points E and M. Expres... | 4.77 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center Q and circumradius 12. Let P be the angle bisector of angle GEQ. Let T be the line through point Q perpendicular to line P. Let V be the midpoint of segment QD. Point M is the reflection of point V across line T. What is the distance between points M and ... | 13.42 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Q and circumradius 5. Point H is the midpoint of segment DF. Let S be the perpendicular bisector of segment HQ. Let W be the line through point B parallel to line S. Point M is the reflection of point A across line W. What is the distance between points M an... | 13.23 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 2. Point W is the reflection of point Y across point A. Let Z be the rotation of point A by angle 5pi/12 around point B. Let J be the circumcircle of polygon ABCDEFGH. Circle T is the reflection of circle J across point B. Point M is... | 2.24 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center M and circumradius 11. Point S is obtained by rotating point E by angle pi about point B. Let Q be the midpoint of segment EM. Point W is the reflection of point B across segment AQ. Point G is the reflection of point S across segment QC. What is the dis... | 54.53 | MATH |
[
{
"content": "Let ABCD be a square with center L and circumradius 12. Let Y be the rotation of point A by angle 2pi/3 around point L. Let V be the rotation of point L by angle pi/3 around point Y. Let Z be the line through point V parallel to segment YB. Let N be the line through point L perpendicular to line Z... | 23.18 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center S and circumradius 4. Let M be the midpoint of segment SA. Let L be the midpoint of segment SF. Point Z is the reflection of point M across point L. Point H is the reflection of point M across segment CA. What is the distance between points Z and H? Express ... | 6.0 | MATH |
[
{
"content": "ABCD is a square with center Z and circumradius 3. Let R be the circumcircle of polygon ABCD. Point J is obtained by rotating point Z by angle pi/6 about point B. Line H is the angle bisector of angle ACJ. Let Q be the reflection of circle R through point A. Point T is the inversion of point C wit... | 10.56 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center W and circumradius 8. Point M is the reflection of point D across segment HG. Point X is the midpoint of segment HG. Let Y be the midpoint of segment XC. What is the length of segment MY? Express your answer as a decimal number rounded to 2 decimal p... | 17.2 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center Q and circumradius 8. Let R be the circumcircle of polygon ABCDEFGHI. Point K is obtained by rotating point E by angle 7pi/12 about point A. Point X is the midpoint of segment KQ. Let Y be the reflection of circle R through point A. Point Z is the inversion... | 6.49 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center K and circumradius 11. Let Q be the line through points H and B. Point Z is on line Q. Let O be the angle bisector of angle ZHC. Point P is the reflection of point G across line O. Line V passes through point D perpendicular to line O. Point X is the refle... | 56.06 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center W and circumradius 12. Point Y is the midpoint of segment CJ. Let M be the perpendicular bisector of segment KI. Point N is the reflection of point Y across line M. Let R be the midpoint of segment YC. Point P is the midpoint of segment NC. What is t... | 4.53 | MATH |
[
{
"content": "ABCD is a square with center Q and circumradius 8. Let T be the rotation of point D by angle pi/12 around point B. Point J is the midpoint of segment QD. Let Y be the perpendicular bisector of segment CT. Let Z be the reflection of point A across point C. Line X passes through point J perpendicula... | 32.55 | MATH |
[
{
"content": "BCDEFG is a regular hexagon with center A and circumradius 5. Let I be the perpendicular bisector of segment EG. Let N be the line through point C perpendicular to line I. Let S be the circumcircle of polygon BCDEFG. Let H be the reflection of circle S across line N. Point O is the inversion of po... | 10.9 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center X and circumradius 7. Let Y be the vector from point D to point C. Let J be the midpoint of segment CB. Let P be the line through points E and A. Let I be point J translated by vector Y. Line T passes through points C and I. Let K be the reflection of line... | 64.56 | MATH |
[
{
"content": "ABCDEFGI is a regular octagon with center H and circumradius 9. Line L is the perpendicular bisector of segment FA. Let W be the line through point B perpendicular to line L. Point P is the reflection of point I across line W. Point Q is the reflection of point P across line L. What is the distanc... | 16.63 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 1. Let N be the line through points H and D. Let J be the line through point E perpendicular to line N. Line Q passes through point G parallel to line J. Point Y is the reflection of point C across line Q. What is the distance betwee... | 2.14 | MATH |
[
{
"content": "ACDEFGHIJKLM is a regular dodecagon with center B and circumradius 11. Let U be the angle bisector of angle KMH. Line R passes through point H parallel to line U. Point S is the reflection of point K across line R. Point Y is the midpoint of segment JS. Find the distance between points Y and M. Ex... | 15.77 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center W and circumradius 9. Let T be the line through points G and A. Line L passes through point W parallel to line T. Line L and segment FE intersect at point P. What is the distance between points P and A? Express your answer as a decimal number rounded to 2 dec... | 14.67 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center J and circumradius 11. Point L is the reflection of point A across point B. Point G is the reflection of point C across point L. Point X is the midpoint of segment AC. Point W is the reflection of point X across point G. What is the length of segment LW? Exp... | 34.35 | MATH |
[
{
"content": "Let BCDEF be a regular 5-gon with center A and circumradius 4. Point M is the reflection of point A across segment FE. Let O be the midpoint of segment FE. Let P be the angle bisector of angle OBM. Point X is the reflection of point A across line P. Find the length of segment XM. Express your answ... | 5.6 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center N and circumradius 4. Point V is the reflection of point B across point A. Let R be the line through points C and V. Point G is the midpoint of segment VF. Point Q is the midpoint of segment VG. Point U is the reflection of point D across line R. Let L be th... | 4.82 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center H and circumradius 9. Let T be the angle bisector of angle DCE. Point N is the reflection of point D across line T. Let L be the midpoint of segment CE. Find the measure of angle DNL, in radians. Express your answer as a decimal number rounded to 2 decim... | 1.31 | MATH |
[
{
"content": "Let ABDEFGHI be a regular octagon with center C and circumradius 5. Let M be the line through points G and I. Let U be the line through point F parallel to line M. Line K is the reflection of line U across point E. Line O passes through point C perpendicular to line U. Let V be the reflection of l... | 5.0 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center P and circumradius 12. Line O is the angle bisector of angle CBE. Line Z is the reflection of line O across point A. Point G lies on line Z at distance 9 from point F. Line L is the reflection of line O across point F. Let W be the reflection of line L acros... | 162.25 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center H and circumradius 1. Line X is the perpendicular bisector of segment BA. Let S be the reflection of line X through point A. Line L is the reflection of line S across point C. Point Z is the midpoint of segment BA. Point G is the reflection of point E acros... | 5.9 | MATH |
[
{
"content": "Let EA = 3. BCDFGH is a regular hexagon with center A and circumradius 12. Let L be the line through point H parallel to segment GA. Point Z is the reflection of point D across line L. Point R is the reflection of point Z across segment GA. Find the length of segment GR. Express your answer as a d... | 36.0 | MATH |
[
{
"content": "Let ABCDEGHIJKL be a regular 11-gon with center F and circumradius 2. Line Z is the perpendicular bisector of segment CE. Let M be the line through point I parallel to line Z. Line P passes through point H parallel to segment CE. Point T is the intersection of lines P and M. What is the distance b... | 2.01 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Q and circumradius 8. Let V be the line through points A and B. Point R is the reflection of point G across line V. Line P is the perpendicular bisector of segment HQ. Point N is the reflection of point F across line P. What is the length of segment NR... | 22.38 | MATH |
[
{
"content": "Let ACDEFGHIJKLM be a regular dodecagon with center B and circumradius 8. Line O passes through points H and E. Let U be the angle bisector of angle BAK. Line X is the reflection of line O across line U. Point N is the reflection of point H across line X. Find the length of segment NE. Express you... | 31.66 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Z and circumradius 3. Point K is obtained by rotating point E by angle 3pi/4 about point C. Let M be the line through points B and C. Let N be the perpendicular bisector of segment DK. Let I be the reflection of line N through point E. Lines M and I intersec... | 13.1 | MATH |
[
{
"content": "Let ABCDFGHI be a regular octagon with center E and circumradius 7. Let O be the midpoint of segment HE. Line L is the angle bisector of angle OIB. Let J be the circumcircle of polygon ABCDFGHI. Circle T is the reflection of circle J across line L. Let Z be the inversion of point F in circle T. Fi... | 3.02 | MATH |
[
{
"content": "ABCD is a square with center S and circumradius 3. Point F is the reflection of point B across point D. Let G be the reflection of point S across point D. Let U be the circumcircle of polygon ABCD. Let N be the inversion of point F in circle U. What is the distance between points N and G? Express ... | 5.0 | MATH |
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