messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "ABCD is a square with center O and circumradius 6. Let F be the line through points A and D. Let E be the line through point C perpendicular to line F. Point T is the reflection of point O across line E. Line Q passes through point T perpendicular to line E. Let J be the midpoint of segment TB. Le... | 18.25 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center V and circumradius 4. Line R passes through point G perpendicular to segment KL. Point Z is the reflection of point E across line R. Line Y passes through points A and G. Let O be the line through points E and Z. Point Q is the intersection of lines ... | 6.77 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Z and circumradius 5. Let W be the circumcircle of polygon ABCDEFGHIJKL. Let M be the reflection of point K across point L. Let Y be the perpendicular bisector of segment ML. Let O be the reflection of circle W across line Y. Point V is the inversion... | 2.16 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Z and circumradius 5. Line K is the angle bisector of angle EAC. Point Y is the midpoint of segment BD. Let Q be the midpoint of segment YD. Let O be the angle bisector of angle EQY. Point J is the reflection of point B across line K. Point W is the reflect... | 17.26 | MATH |
[
{
"content": "ABCDEFGHIJKM is a regular dodecagon with center L and circumradius 7. Point T is the midpoint of segment GK. Let Y be the midpoint of segment DT. Find the length of segment IY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 8.46 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center S and circumradius 2. Let O be the perpendicular bisector of segment BJ. Let W be the circumcircle of polygon ABCDEFGHIJK. Let Z be the line through point F perpendicular to line O. Let T be the reflection of circle W across line Z. Let Q be the inve... | 2.1 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Q and circumradius 4. Let V be the circumcircle of polygon ABCDEFGHIJKL. Let M be the reflection of circle V through point B. Point S is the midpoint of segment BJ. Let P be the inversion of point E in circle M. Find the distance between points P and... | 5.96 | MATH |
[
{
"content": "Let BCDEFG be a regular hexagon with center A and circumradius 12. Point V is the reflection of point F across point G. Let Z be the circumcircle of polygon BCDEFG. Circle K is the reflection of circle Z across point F. Let S be the reflection of circle K through point A. Line I is the angle bisec... | 27.57 | MATH |
[
{
"content": "Let ACDEFGHI be a regular octagon with center B and circumradius 12. Line K is the perpendicular bisector of segment EC. Point U is the midpoint of segment HB. Line V is the reflection of line K across point I. Point Z is on line V. Let J be the midpoint of segment UZ. Find the measure of angle DC... | 1.96 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center W and circumradius 1. Point Y is obtained by rotating point D by angle 2pi/3 about point E. Point N is the reflection of point G across point C. Let O be the line through points H and A. Let T be the perpendicular bisector of segment CN. Point X ... | 3.86 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 6. Point Z is obtained by rotating point E by angle 3pi/4 about point F. Let J be the circumcircle of polygon ABCDEFGH. Circle Q is the reflection of circle J across point C. Let O be the line through points E and Z. Let S be the ref... | 14.45 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 12. Let J be the line through points D and H. Let X be the reflection of point C across point H. Point M is the midpoint of segment CF. Point Z is the reflection of point M across line J. Find the length of segment XZ. Express your a... | 38.13 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Y and circumradius 1. Point O is obtained by rotating point C by angle 11pi/12 about point D. Point G is the midpoint of segment DC. Let U be the midpoint of segment OG. Point X is the midpoint of segment ED. Point H is the reflection of point Y across poin... | 0.82 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 12. Point Q is the midpoint of segment CE. Point M is the reflection of point Q across point F. Point N is the reflection of point B across segment DC. Find the length of segment MN. Express your answer as a decimal number rounded to 2... | 51.26 | MATH |
[
{
"content": "Let ABCDEFGHIJKM be a regular dodecagon with center L and circumradius 12. Point T is obtained by rotating point D by angle pi/4 about point J. Let P be the midpoint of segment KG. Point Q is the midpoint of segment TL. Let X be the circumcircle of polygon ABCDEFGHIJKM. Point W is the inversion of... | 23.53 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center U and circumradius 2. Point Y is the midpoint of segment KC. Line M is the perpendicular bisector of segment YG. Point O is the reflection of point F across line M. Let R be the midpoint of segment YG. Point V is the reflection of point O across ... | 1.59 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 7. Point I is obtained by rotating point E by angle 2pi/3 about point G. Line N is the angle bisector of angle GBI. Let X be the reflection of line N through point H. Point Z is the reflection of point A across line X. Let M be the r... | 8.74 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center W and circumradius 7. Let Q be the perpendicular bisector of segment HJ. Let V be the line through point W perpendicular to line Q. Let U be the reflection of line V through point E. Point P is the reflection of point A across line U. What is the length o... | 22.65 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 11. Let I be the perpendicular bisector of segment EC. Let U be the midpoint of segment FD. Point X is the reflection of point U across line I. Find the length of segment AX. Express your answer as a decimal number rounded to 2 decimal... | 14.55 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center X and circumradius 12. Line N is the angle bisector of angle CHG. Line U passes through point B perpendicular to line N. Let W be the line through point D parallel to line U. Point Z is the reflection of point E across line W. Find the length of segme... | 18.52 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center U and circumradius 3. Point O is the reflection of point A across point C. Let Y be the midpoint of segment BO. Point N is the midpoint of segment CY. Point T is the midpoint of segment CN. What is the length of segment TD? Express your answer as a decimal numb... | 3.89 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center M and circumradius 12. Line Z passes through points D and E. Let I be the midpoint of segment DA. Point Q is the reflection of point B across line Z. Let N be the midpoint of segment AQ. What is the length of segment IN? Express your answer as a decimal number ... | 11.41 | MATH |
[
{
"content": "BCDEFG is a regular hexagon with center A and circumradius 1. Let P be the perpendicular bisector of segment DB. Point L is the midpoint of segment DA. Point T is the reflection of point L across line P. Point Y is the reflection of point A across point B. Find the length of segment TY. Express yo... | 1.5 | MATH |
[
{
"content": "ABCDEGHI is a regular octagon with center F and circumradius 9. Let Y be the angle bisector of angle BID. Point Q is the reflection of point H across line Y. Line U is the reflection of line Y across point F. Let P be the reflection of point Q across point H. Line U and segment AG intersect at poi... | 19.08 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center U and circumradius 8. Let Q be the midpoint of segment UE. Let X be the midpoint of segment HB. Let O be the circumcircle of polygon ABCDEFGH. Point L is obtained by rotating point Q by angle 11pi/12 about point B. Line M passes through points B and L. Lin... | 9.21 | MATH |
[
{
"content": "ABCDEFGHJKLM is a regular dodecagon with center I and circumradius 11. Let R be the reflection of point M across point D. Line O is the angle bisector of angle IDB. Line Y passes through points R and K. Let X be the reflection of line O through point G. Line Q passes through point L perpendicular ... | 22.37 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center X and circumradius 11. Point K is the midpoint of segment XH. Let V be the circumcircle of polygon ABCDEFGHIJ. Let O be the angle bisector of angle XAH. Point L is the reflection of point E across line O. Let W be the reflection of circle V through po... | 30.36 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Z and circumradius 11. Point Y is the reflection of point A across point D. Point W is the reflection of point E across point Y. Point K is the midpoint of segment DB. Let H be the reflection of point K across point Z. Find the length of segment WH. Expr... | 64.84 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center M and circumradius 6. Point K is the midpoint of segment GC. Point N is obtained by rotating point G by angle 3pi/4 about point F. Line Y is the perpendicular bisector of segment GD. Let X be the reflection of line Y through point A. Line Z passes through... | 10.57 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 3. Let G be the circumcircle of polygon ABCDF. Line T is the angle bisector of angle DFE. Point H is the reflection of point F across point C. Let P be the reflection of circle G across line T. Let Y be the inversion of point C in circle P. F... | 6.88 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center U and circumradius 9. Point Y is obtained by rotating point C by angle pi/4 about point A. Let N be the midpoint of segment BG. Line X passes through points D and C. Let I be the line through point Y parallel to line X. Point Q is the reflection of point ... | 8.47 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center L and circumradius 9. Let R be the reflection of point L across point B. Line V passes through points D and E. Let S be the circumcircle of polygon ABCDEFGHIJ. Let P be the reflection of circle S across line V. Point U is the inversion of point R with... | 4.87 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center P and circumradius 10. Let Z be the circumcircle of polygon ABCDEFGH. Let S be the perpendicular bisector of segment CD. Let I be the reflection of circle Z through point G. Line N passes through point D parallel to line S. Line X is the reflection of line... | 34.6 | MATH |
[
{
"content": "Let ACDEF be a regular 5-gon with center B and circumradius 4. Let W be the line through points E and C. Let V be the line through point B parallel to line W. Segment CF and line V intersect at point H. Find the distance between points D and H. Express your answer as a decimal number rounded to 2 ... | 4.52 | MATH |
[
{
"content": "Let ABCDEFHI be a regular octagon with center G and circumradius 2. Let R be the reflection of point A across point I. Line Q is the perpendicular bisector of segment DR. Line X is the reflection of line Q across point B. Point Z is the reflection of point A across line X. Point U is the reflectio... | 1.53 | MATH |
[
{
"content": "ABDEFG is a regular hexagon with center C and circumradius 1. Point L is the midpoint of segment AB. Point N is the midpoint of segment GL. Let W be the midpoint of segment DN. Find the length of segment BW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer... | 0.7 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center M and circumradius 7. Point S is the midpoint of segment BF. Point N is the reflection of point S across segment AE. Point K is the reflection of point C across segment AE. What is the distance between points K and N? Express your answer as a decimal number... | 6.12 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center M and circumradius 3. Let L be the circumcircle of polygon ABCDEFGH. Line N is the perpendicular bisector of segment GE. Let I be the line through point H parallel to line N. Circle Z is the reflection of circle L across line I. Point W is the inversion of... | 0.39 | MATH |
[
{
"content": "Let ACDEFGHI be a regular octagon with center B and circumradius 9. Let O be the circumcircle of polygon ACDEFGHI. Point N is the midpoint of segment IH. Line Z passes through points A and N. Point M is the reflection of point H across line Z. Point Y is the inversion of point N with respect to ci... | 2.31 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center O and circumradius 7. Point X is the reflection of point O across point B. Let P be the midpoint of segment XJ. Point W is the midpoint of segment CF. Let V be the angle bisector of angle BPW. Point N is the reflection of point B across line V. Find the l... | 1.77 | MATH |
[
{
"content": "ABCD is a square with center M and circumradius 5. Let S be the line through points C and M. Line P is the perpendicular bisector of segment AB. Line V is the reflection of line S across line P. Point Y is the midpoint of segment DA. Point H is on line S with |HD| = 11. Let Q be the midpoint of se... | 8.02 | MATH |
[
{
"content": "Let ABCDEFHI be a regular octagon with center G and circumradius 8. Point L is the midpoint of segment GB. Let M be the circumcircle of polygon ABCDEFHI. Let P be the angle bisector of angle LHD. Point V is the reflection of point A across line P. Let Z be the inversion of point V in circle M. Wha... | 13.5 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Z and circumradius 6. Let S be the reflection of point Z across point B. Point L is the midpoint of segment DA. Point U is the reflection of point E across point L. Let I be the midpoint of segment SE. What is the distance between points I and U? Express yo... | 3.55 | MATH |
[
{
"content": "ABCDEFGHIJKM is a regular dodecagon with center L and circumradius 5. Let X be the circumcircle of polygon ABCDEFGHIJKM. Let O be the reflection of circle X through point E. Line S passes through points M and D. Let Y be the inversion of point L in circle O. Point Z is the reflection of point Y ac... | 8.14 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center T and circumradius 3. Point K is the midpoint of segment BT. Let R be the circumcircle of polygon ABCDEFGHIJ. Let U be the inversion of point K in circle R. Find the distance between points U and B. Express your answer as a decimal number rounded to 2 dec... | 3.0 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center X and circumradius 6. Let L be the perpendicular bisector of segment DF. Line Q passes through point F parallel to line L. Point S is the reflection of point D across line Q. Let H be the line through points E and S. Lines Q and H intersect at point Z. P... | 10.39 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center R and circumradius 11. Let J be the vector from point A to point F. Point Q is obtained by rotating point B by angle pi/3 about point H. Point W is the translation of point R by vector J. Line T is the perpendicular bisector of segment BR. Point S is t... | 46.7 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 10. Let T be the reflection of point G across point C. Let L be the line through point G parallel to segment AH. Line V passes through point T perpendicular to line L. Point I is the reflection of point G across line V. Find the dist... | 74.31 | MATH |
[
{
"content": "Let ABCDFG be a regular hexagon with center E and circumradius 2. Let T be the circumcircle of polygon ABCDFG. Let W be the angle bisector of angle DAE. Point K is the midpoint of segment BC. Let S be the reflection of circle T through point K. Point R is the inversion of point D with respect to c... | 4.36 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center J and circumradius 7. Line U passes through points G and E. Line S passes through point F perpendicular to line U. Let Y be the line through point F perpendicular to line S. Point Q is the reflection of point B across line Y. What is the length of segment QA?... | 22.19 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center H and circumradius 2. Line T passes through points E and C. Line N passes through point A perpendicular to line T. Point G is the reflection of point E across line N. Let K be the reflection of point C across point D. Point R is the reflection of point B ac... | 4.16 | MATH |
[
{
"content": "ABCDFGHI is a regular octagon with center E and circumradius 12. Line N passes through points G and C. Point J is the reflection of point B across line N. Let R be the line through points C and E. Line W is the reflection of line R across line N. Let Z be the reflection of line W through point A. ... | 16.97 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center W and circumradius 4. Let S be the midpoint of segment BD. Point J is the midpoint of segment FE. Line Z passes through points W and J. Let K be the line through point A parallel to line Z. Point V is the reflection of point S across line K. Find the distanc... | 7.21 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center U and circumradius 5. Point G is the midpoint of segment AU. Point Y is obtained by rotating point A by angle 5pi/12 about point U. Point O is the midpoint of segment BE. Line K passes through points C and D. Point I is the reflection of point O across line... | 11.78 | MATH |
[
{
"content": "ABDEFG is a regular hexagon with center C and circumradius 4. Let Y be the rotation of point F by angle 3pi/4 around point A. Let X be the angle bisector of angle FYG. Point L is the reflection of point F across line X. Point P is the reflection of point L across segment YF. What is the length of ... | 12.8 | MATH |
[
{
"content": "Let BCDEFGHIJKLM be a regular dodecagon with center A and circumradius 6. Let T be the line through points D and B. Point P is the reflection of point K across line T. Let Q be the midpoint of segment JP. Find the length of segment CQ. Express your answer as a decimal number rounded to 2 decimal p... | 4.52 | MATH |
[
{
"content": "Let TG = 9. ABCDEF is a regular hexagon with center G and circumradius 10. Let H be the rotation of point G by angle pi around point D. Point W is the midpoint of segment AG. Point M is the midpoint of segment HW. Line V passes through points G and A. Point Q is the midpoint of segment MF. Point I... | 7.6 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center L and circumradius 12. Let T be the line through points B and F. Line J passes through point D parallel to line T. Let O be the reflection of line T through point A. Line Q is the reflection of line J across line T. Line R is the reflection of line O acros... | 12.35 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center T and circumradius 7. Let P be the rotation of point A by angle 5pi/12 around point E. Point I is the midpoint of segment FT. Point J is the reflection of point A across segment PI. Point R is the reflection of point J across point P. What is the distance be... | 29.78 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center T and circumradius 3. Let U be the rotation of point G by angle 3pi/4 around point B. Let O be the circumcircle of polygon ABCDEFGHIJK. Circle P is the reflection of circle O across point F. Line S is the perpendicular bisector of segment TU. Let Y be th... | 12.07 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center R and circumradius 4. Point X is the reflection of point F across point A. Let I be the line through points B and H. Point T is the reflection of point C across line I. Point Q is the reflection of point G across point X. What is the measure of angle T... | 0.39 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center U and circumradius 1. Line Y passes through point F parallel to segment HU. Line K passes through points D and A. Let N be the reflection of line K through point E. Lines Y and N intersect at point I. Find the distance between points I and E. Express y... | 1.33 | MATH |
[
{
"content": "Let ABCDEGHI be a regular octagon with center F and circumradius 11. Let K be the circumcircle of polygon ABCDEGHI. Line N is the angle bisector of angle GIA. Let T be the angle bisector of angle IBC. Point W is the reflection of point H across line T. Let V be the reflection of circle K across li... | 28.32 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center P and circumradius 10. Line M passes through points C and A. Line L is the perpendicular bisector of segment EF. Let J be the reflection of line L through point E. Lines M and J intersect at point O. Find the distance between points O and F. Express your... | 25.17 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 10. Point U is obtained by rotating point Y by angle 3pi/4 about point F. Let P be the circumcircle of polygon ABCDEFGH. Let Q be the reflection of point C across point U. Point T is the inversion of point Q with respect to circle P.... | 14.41 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Q and circumradius 4. Let M be the circumcircle of polygon ABCDEFGHIJKL. Point P is the reflection of point B across point I. Point V is the reflection of point I across point P. Point U is the inversion of point P with respect to circle M. What ... | 17.97 | MATH |
[
{
"content": "ABCD is a square with center K and circumradius 1. Point E is the reflection of point K across segment DC. Let X be the reflection of point E across point C. Let H be the midpoint of segment KD. Find the distance between points H and X. Express your answer as a decimal number rounded to 2 decimal ... | 1.8 | MATH |
[
{
"content": "ABCD is a square with center Y and circumradius 4. Point T is the midpoint of segment CY. Let L be the midpoint of segment TB. Point V is the reflection of point C across point D. Let E be the reflection of point L across point A. Point W is the midpoint of segment EV. What is the length of segmen... | 11.1 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center H and circumradius 12. Line J passes through points C and B. Point I is the reflection of point H across line J. Let S be the reflection of point F across point I. Point W is the reflection of point S across line J. What is the distance between points W ... | 41.57 | MATH |
[
{
"content": "ABCD is a square with center M and circumradius 2. Let W be the midpoint of segment BA. Let V be the midpoint of segment MW. Let H be the reflection of point A across point V. Point U is the midpoint of segment AV. What is the length of segment UH? Express your answer as a decimal number rounded t... | 2.37 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center S and circumradius 8. Let J be the angle bisector of angle DBE. Let I be the line through point D perpendicular to line J. Line K passes through point G parallel to line J. Point Z is the midpoint of segment SF. Line T passes through points Z and C. Let P be ... | 6.59 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center X and circumradius 5. Let P be the line through points C and E. Let G be the midpoint of segment BC. Point L is the reflection of point G across line P. Find the distance between points X and L. Express your answer as a decimal number rounded to 2 decimal place... | 5.8 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center M and circumradius 3. Let G be the reflection of point M across point C. Let O be the midpoint of segment BG. Line T passes through points B and D. Point F is the reflection of point O across line T. Let W be the midpoint of segment AM. Find the length of s... | 0.67 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center O and circumradius 1. Line R is the perpendicular bisector of segment BF. Let T be the line through point C parallel to line R. Point Q is the reflection of point F across line T. Let Y be the reflection of point Q across point C. Find the length of segmen... | 3.7 | MATH |
[
{
"content": "Let ABDEFGH be a regular 7-gon with center C and circumradius 1. Let J be the circumcircle of polygon ABDEFGH. Let M be the reflection of circle J through point E. Point R is the reflection of point C across point A. Let Y be the inversion of point C in circle M. What is the distance between point... | 3.41 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center X and circumradius 7. Line Z is the perpendicular bisector of segment HI. Let U be the line through point L parallel to line Z. Point Y is the reflection of point H across line U. Point T is the reflection of point X across point D. What is the dista... | 30.24 | MATH |
[
{
"content": "ABCDEGH is a regular 7-gon with center F and circumradius 3. Let Z be the rotation of point E by angle pi/3 around point B. Let M be the reflection of point F across point C. Let X be the reflection of point A across point Z. Let P be the reflection of point X across point E. Point Y is the reflec... | 6.59 | MATH |
[
{
"content": "ABCD is a square with center F and circumradius 4. Line L passes through points D and B. Line Q passes through point A perpendicular to line L. Line H is the reflection of line Q across point D. Let G be the reflection of point D across point A. Line O is the reflection of line H across point B. L... | 76.11 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center V and circumradius 7. Let L be the angle bisector of angle BDH. Line R passes through point E parallel to line L. Line R and segment FA intersect at point M. Let T be the midpoint of segment FA. What is the distance between points M and T? Express your ... | 2.11 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center O and circumradius 1. Point L is the midpoint of segment IG. Point T is obtained by rotating point A by angle pi/2 about point D. Let M be the circumcircle of polygon ABCDEFGHIJ. Point P is the reflection of point J across segment BA. Let N be the inv... | 1.1 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center X and circumradius 12. Let R be the line through points K and D. Point U is the reflection of point E across line R. Point S is the intersection of line R and segment BX. What is the length of segment US? Express your answer as a decimal number round... | 12.42 | MATH |
[
{
"content": "YE = 3. Let ABCDFGHIJKL be a regular 11-gon with center E and circumradius 7. Point X is the midpoint of segment FE. Let U be the angle bisector of angle CKJ. Let R be the reflection of line U through point X. Point S is the reflection of point X across line R. What is the distance between points ... | 3.28 | MATH |
[
{
"content": "ABCEFGHI is a regular octagon with center D and circumradius 5. Line U is the perpendicular bisector of segment AI. Let M be the midpoint of segment HI. Let V be the reflection of line U through point E. Segment GB and line V intersect at point X. What is the distance between points X and M? Expre... | 7.29 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center L and circumradius 5. Line O is the angle bisector of angle LDB. Let M be the circumcircle of polygon ABCDEF. Let Z be the line through point B perpendicular to line O. Circle N is the reflection of circle M across line Z. Point Y is the inversion of point E... | 14.98 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Q and circumradius 7. Let X be the line through points F and A. Line T passes through point Q parallel to segment FD. Let P be the reflection of line X through point C. Let H be the midpoint of segment FD. Lines T and P intersect at point K. Find the distanc... | 18.52 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center J and circumradius 8. Point P is obtained by rotating point J by angle pi/6 about point H. Let R be the line through points D and A. Line N passes through point G perpendicular to segment PA. Line Z is the reflection of line R across line N. Line S is the r... | 11.43 | MATH |
[
{
"content": "Let EP = 3. Let ABCDFG be a regular hexagon with center P and circumradius 6. Let L be the line through points F and D. Point X is the reflection of point B across line L. Point R is the midpoint of segment XG. Point O is the midpoint of segment DB. Find the measure of angle RDO, in radians. Expre... | 2.09 | MATH |
[
{
"content": "ABCDEFGHIKL is a regular 11-gon with center J and circumradius 2. Let V be the rotation of point A by angle 5pi/12 around point E. Let Y be the midpoint of segment EF. Line R passes through points Y and I. Line T passes through point G perpendicular to line R. Line O passes through point J perpend... | 4.2 | MATH |
[
{
"content": "Let ABDEFGHIJKLM be a regular dodecagon with center C and circumradius 1. Point W is the reflection of point B across point I. Point N is the reflection of point A across point B. Point O is the reflection of point N across segment WG. What is the distance between points K and O? Express your answ... | 3.21 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center M and circumradius 6. Line I passes through points E and B. Let O be the circumcircle of polygon ABCDEFG. Let Q be the reflection of circle O across line I. Line R is the reflection of line I across point G. Circle N is the reflection of circle Q across l... | 24.82 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center X and circumradius 6. Let N be the reflection of point C across point E. Let T be the angle bisector of angle NBA. Point J is the reflection of point D across point F. Point R is the reflection of point I across line T. What is the distance between points R... | 10.8 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center P and circumradius 12. Point N is the midpoint of segment IK. Point Z is the midpoint of segment AC. Let T be the midpoint of segment NB. Find the length of segment ZT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the a... | 6.94 | MATH |
[
{
"content": "ACDEF is a regular 5-gon with center B and circumradius 8. Let G be the circumcircle of polygon ACDEF. Let W be the midpoint of segment FB. Let U be the midpoint of segment DB. Let L be the inversion of point W in circle G. Point S is the midpoint of segment UB. What is the distance between points... | 17.66 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center X and circumradius 6. Line Q passes through points B and D. Point S is the reflection of point X across line Q. Line N passes through points S and A. Point Y is the intersection of lines N and Q. Find the length of segment YE. Express your answer as a decimal n... | 7.96 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 10. Line R is the angle bisector of angle FDC. Let P be the reflection of point G across point F. Line V is the angle bisector of angle BPG. Point L is the midpoint of segment BC. Point K is the reflection of point L across line R. P... | 9.81 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Z and circumradius 12. Let P be the midpoint of segment FE. Let W be the line through points E and D. Point K is the midpoint of segment CZ. Let X be the reflection of line W through point P. Point Q is the reflection of point D across line X. What is ... | 4.3 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center X and circumradius 1. Let I be the circumcircle of polygon ABCDEF. Let T be the reflection of point A across point C. Point O is the inversion of point T with respect to circle I. Point U is the midpoint of segment XB. Find the distance between points U and ... | 0.57 | MATH |
[
{
"content": "Let ABDEFGHIJK be a regular 10-gon with center C and circumradius 6. Line U passes through points J and C. Let O be the line through points B and D. Point Y is the intersection of lines O and U. Point T is the midpoint of segment AY. What is the distance between points C and T? Express your answer... | 4.85 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center K and circumradius 7. Let Q be the midpoint of segment HF. Point P is the midpoint of segment KQ. Point Y is the reflection of point P across segment FK. Find the length of segment YQ. Express your answer as a decimal number rounded to 2 decimal places.\n\... | 5.53 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center S and circumradius 5. Point M is the midpoint of segment SB. Line I is the perpendicular bisector of segment MF. Point L is the reflection of point E across segment AF. Point X is the reflection of point L across line I. What is the distance between points S... | 7.38 | MATH |
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