messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let ABCDFGHIJKL be a regular 11-gon with center E and circumradius 8. Let U be the circumcircle of polygon ABCDFGHIJKL. Circle W is the reflection of circle U across point H. Let N be the reflection of circle W through point D. Let M be the reflection of circle N through point G. Let T be the inve... | 30.35 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center W and circumradius 5. Line S passes through points J and C. Line T passes through point F parallel to line S. Line O passes through points A and K. Point Y is the intersection of lines O and T. Find the distance between points Y and W. Express your a... | 33.71 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 12. Let I be the midpoint of segment OE. Let Q be the line through points B and I. Let H be the line through point F perpendicular to line Q. Let U be the reflection of point E across point C. Let N be the line through points U and A. Let ... | 1.05 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center O and circumradius 7. Let U be the reflection of point G across point F. Line Y passes through point U perpendicular to segment OH. Let V be the circumcircle of polygon ABCDEFGH. Circle X is the reflection of circle V across line Y. Line L passes throu... | 15.32 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center Y and circumradius 11. Line Q passes through point G parallel to segment YC. Line V passes through points C and B. Lines V and Q intersect at point N. Point P is the midpoint of segment FN. Find the length of segment PN. Express your answer as a decimal n... | 10.46 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Z and circumradius 10. Let N be the circumcircle of polygon ABCDEF. Let X be the midpoint of segment BZ. Let H be the inversion of point X in circle N. Find the length of segment HD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPre... | 26.46 | MATH |
[
{
"content": "Let ABCDEFGHIJLM be a regular dodecagon with center K and circumradius 10. Point R is the reflection of point H across segment GL. Point O is the intersection of segments RI and GL. Point Q is the midpoint of segment FI. Find the distance between points O and Q. Express your answer as a decimal nu... | 2.11 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center W and circumradius 12. Point U is the reflection of point A across point E. Let X be the midpoint of segment KW. Point O is obtained by rotating point X by angle 7pi/12 about point F. Line S passes through point C parallel to segment KO. Line S a... | 8.13 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center X and circumradius 1. Let R be the reflection of point A across point E. Let Z be the midpoint of segment XA. Point U is the reflection of point B across point X. Point N is the midpoint of segment ZR. Let Q be the midpoint of segment UN. Find the length of... | 0.18 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center K and circumradius 2. Let I be the angle bisector of angle HCE. Line U passes through point D parallel to line I. Let R be the reflection of line U through point E. Point Z is the reflection of point C across line R. What is the distance between points... | 4.57 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center V and circumradius 5. Let U be the perpendicular bisector of segment HF. Line S passes through point A parallel to line U. Point Y is the reflection of point H across line S. Let Q be the reflection of point B across point Y. Point X is the reflection of p... | 12.38 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 3. Let V be the line through points B and E. Let M be the angle bisector of angle DEG. Line I is the reflection of line M across line V. Line T passes through points D and G. Point Z is the intersection of lines T and I. Find the dis... | 3.08 | MATH |
[
{
"content": "Let BCDEFG be a regular hexagon with center A and circumradius 8. Let X be the reflection of point G across point C. Line I passes through points X and F. Point K is the reflection of point G across point F. Point J is the reflection of point F across point C. Line S passes through point K perpend... | 26.23 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center W and circumradius 12. Let J be the midpoint of segment WE. Point U is the reflection of point D across point W. Point O is the midpoint of segment UJ. Let K be the perpendicular bisector of segment CO. Point R is the reflection of point B across line K. What i... | 19.09 | MATH |
[
{
"content": "ABCDEGHIJK is a regular 10-gon with center F and circumradius 12. Point M is the midpoint of segment AH. Let N be the midpoint of segment JF. Point Y is the reflection of point M across segment GN. What is the length of segment BY? Express your answer as a decimal number rounded to 2 decimal place... | 16.99 | MATH |
[
{
"content": "Let ABCD be a square with center G and circumradius 1. Let E be the circumcircle of polygon ABCD. Line U is the angle bisector of angle GCB. Point P is the reflection of point A across line U. Let N be the line through point P parallel to line U. Circle I is the reflection of circle E across line ... | 1.53 | MATH |
[
{
"content": "ABCEFGHIJKL is a regular 11-gon with center D and circumradius 3. Point T is the reflection of point K across segment JG. Let N be the perpendicular bisector of segment TB. Let Z be the line through point C parallel to segment KF. Point R is the reflection of point J across line Z. Point Y is the ... | 5.77 | MATH |
[
{
"content": "Let ABCDFGHI be a regular octagon with center E and circumradius 3. Line Q passes through points G and A. Line Z passes through point B parallel to segment IA. Point M is the intersection of lines Z and Q. What is the measure of angle ADM, in radians? Express your answer as a decimal number rounde... | 0.39 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Y and circumradius 9. Let R be the line through points A and E. Line T is the reflection of line R across point D. Point G is the reflection of point F across line T. Point K is the midpoint of segment YA. Point X is the reflection of point C across poin... | 20.69 | MATH |
[
{
"content": "Let ABCDEFGHIJLM be a regular dodecagon with center K and circumradius 7. Let O be the reflection of point B across point L. Point V is the midpoint of segment KJ. Point W is the reflection of point O across segment DG. Find the distance between points W and V. Express your answer as a decimal num... | 25.35 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center X and circumradius 7. Let R be the circumcircle of polygon ABCDEFGH. Line K passes through points B and H. Point I is the reflection of point A across line K. Point S is the inversion of point I with respect to circle R. Find the distance between points S ... | 18.29 | MATH |
[
{
"content": "BCDEFG is a regular hexagon with center A and circumradius 7. Point N is the midpoint of segment GB. Let S be the reflection of point N across point F. Line X passes through points G and E. Point R is the reflection of point S across line X. What is the length of segment RE? Express your answer as... | 10.5 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center I and circumradius 4. Let L be the midpoint of segment GD. Let W be the midpoint of segment LI. Line P passes through points W and B. Line P and segment GE intersect at point M. Find the distance between points B and M. Express your answer as a decimal num... | 6.84 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center U and circumradius 4. Let M be the midpoint of segment DB. Line Q is the angle bisector of angle JIG. Point N is the reflection of point M across line Q. Point O is the midpoint of segment NJ. Find the distance between points U and O. Express your ans... | 1.31 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center X and circumradius 5. Line N passes through point X perpendicular to segment XK. Point U is the reflection of point A across line N. Line O passes through point U perpendicular to segment XK. Let W be the reflection of point G across point F. Point Q is ... | 7.29 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center N and circumradius 10. Point S is the reflection of point K across point E. Let R be the angle bisector of angle AJK. Point X is the reflection of point S across line R. Point Q is the reflection of point X across point H. Find the length of segment ... | 56.03 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center L and circumradius 12. Line S is the perpendicular bisector of segment LG. Line K is the reflection of line S across point H. Point V is the reflection of point F across line K. What is the distance between points V and C? Express your answer as a deci... | 26.83 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center I and circumradius 3. Let N be the perpendicular bisector of segment IB. Point M is the reflection of point C across line N. Point L is the midpoint of segment IC. Point U is the reflection of point M across point L. What is the length of segment EU? Expres... | 2.18 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center T and circumradius 6. Let Y be the reflection of point D across point A. Line Z is the angle bisector of angle HFY. Point O is the midpoint of segment CK. Point P is the reflection of point O across line Z. What is the length of segment OP? Express y... | 10.92 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center M and circumradius 5. Line W is the angle bisector of angle GAM. Let Z be the rotation of point I by angle pi/12 around point D. Point V lies on line W at distance 4 from point F. Line L is the angle bisector of angle JEZ. Let P be the reflection of line ... | 16.14 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center J and circumradius 1. Let V be the midpoint of segment CD. Let M be the midpoint of segment AC. Find the length of segment MV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 0.95 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center J and circumradius 3. Let M be the rotation of point A by angle pi/12 around point F. Let P be the line through points A and M. Let T be the circumcircle of polygon ABCDEF. Circle U is the reflection of circle T across line P. Point I is the inversion of poi... | 7.65 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center N and circumradius 8. Let V be the circumcircle of polygon ABCDEFGHIJKL. Line Y passes through points I and A. Point Z is the midpoint of segment NC. Let W be the perpendicular bisector of segment DC. Let U be the reflection of line W across line Y. ... | 2.88 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 4. Let N be the midpoint of segment BC. Let W be the perpendicular bisector of segment EF. Point M is the reflection of point A across line W. Point I is the reflection of point A across point M. What is the length of segment NI? Express your... | 8.43 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center W and circumradius 6. Let H be the line through points B and A. Point X is the reflection of point A across point E. Line T is the reflection of line H across point W. Line M is the reflection of line H across line T. Point Y is the reflection of point X ac... | 99.66 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center V and circumradius 5. Let W be the perpendicular bisector of segment BE. Line P passes through point C perpendicular to line W. Let U be the reflection of point F across point A. Point M is the reflection of point K across line P. What is the distance be... | 15.04 | MATH |
[
{
"content": "ABCDEFGIJ is a regular 9-gon with center H and circumradius 8. Let R be the perpendicular bisector of segment AI. Line P is the reflection of line R across point B. Let Q be the line through point A perpendicular to line P. Point O is the reflection of point E across line Q. What is the distance b... | 13.86 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center S and circumradius 3. Point P is the midpoint of segment SB. Let F be the reflection of point C across point S. Let W be the angle bisector of angle APE. Point K is the reflection of point F across line W. Find the length of segment PK. Express your answer as a... | 3.75 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center X and circumradius 9. Point W is the reflection of point E across point C. Let L be the angle bisector of angle WFX. Line S passes through point B parallel to line L. Let T be the reflection of line S across line L. Line Y is the reflection of line T ac... | 31.07 | MATH |
[
{
"content": "Let ABDEFGHI be a regular octagon with center C and circumradius 6. Point Y is the midpoint of segment IG. Point O is the reflection of point Y across segment BD. Point R is the midpoint of segment OY. What is the distance between points A and R? Express your answer as a decimal number rounded to ... | 5.09 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center J and circumradius 3. Line V passes through point J parallel to segment CE. Point H is the midpoint of segment AE. Line T passes through points D and H. Let O be the circumcircle of polygon ABCDE. Let Q be the line through points D and C. Circle X is the reflec... | 9.22 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center V and circumradius 11. Let Q be the circumcircle of polygon ABCDEFGHIJKL. Let P be the midpoint of segment GF. Let X be the midpoint of segment GI. Point R is the inversion of point P with respect to circle Q. What is the distance between points R an... | 8.19 | MATH |
[
{
"content": "BCDEFG is a regular hexagon with center A and circumradius 11. Let R be the line through points A and G. Line Q passes through points C and B. Line K is the reflection of line R across line Q. Point P is the reflection of point D across line K. What is the measure of angle PBE, in radians? Express... | 2.09 | MATH |
[
{
"content": "ABCDEFHIJKL is a regular 11-gon with center G and circumradius 1. Let N be the midpoint of segment KL. Let X be the midpoint of segment EC. Let P be the line through point K perpendicular to segment NX. Let Z be the midpoint of segment NX. Let W be the reflection of point L across point C. Point O... | 8.0 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center M and circumradius 3. Line Y is the angle bisector of angle BEM. Let R be the line through point M parallel to line Y. Line O passes through points A and F. Lines R and O intersect at point Q. What is the distance between points Q and C? Express your a... | 6.06 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center V and circumradius 1. Point L is the reflection of point F across point J. Line X passes through points A and K. Let N be the line through point I parallel to line X. Point M is the reflection of point L across line N. Find the distance between point... | 1.72 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center M and circumradius 9. Let V be the line through points F and E. Let P be the angle bisector of angle AFG. Let Z be the perpendicular bisector of segment CI. Point N is the reflection of point I across line V. Let Q be the reflection of point C across point ... | 15.59 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center S and circumradius 10. Point T is the midpoint of segment BF. Point W is the reflection of point S across point C. Let X be the midpoint of segment DT. Find the length of segment XW. Express your answer as a decimal number rounded to 2 decimal places.\n\n... | 17.84 | MATH |
[
{
"content": "ABCDEGHI is a regular octagon with center F and circumradius 2. Let L be the reflection of point G across point I. Let V be the line through points L and H. Point K is the reflection of point D across line V. Point U is the reflection of point G across line V. Let T be the midpoint of segment AU. ... | 3.14 | MATH |
[
{
"content": "ABDEFGHIJKLM is a regular dodecagon with center C and circumradius 8. Let R be the circumcircle of polygon ABDEFGHIJKLM. Let P be the perpendicular bisector of segment AC. Circle X is the reflection of circle R across line P. Let W be the line through point I perpendicular to line P. Point O is th... | 10.94 | MATH |
[
{
"content": "Let ABDEF be a regular 5-gon with center C and circumradius 2. Point L is the reflection of point A across point E. Let H be the midpoint of segment LB. Point X is the midpoint of segment HD. What is the distance between points X and L? Express your answer as a decimal number rounded to 2 decimal ... | 4.32 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Q and circumradius 10. Point H is the reflection of point Q across point E. Let Z be the angle bisector of angle ECA. Point G is the reflection of point H across line Z. Point I is the reflection of point C across point G. Find the length of segment DI. ... | 55.68 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center K and circumradius 2. Point R is the reflection of point E across point A. Point W is the reflection of point K across point A. Line J is the perpendicular bisector of segment WR. Point I is the reflection of point C across line J. Find the length of seg... | 6.0 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center N and circumradius 8. Let O be the line through points B and G. Let M be the midpoint of segment AD. Let L be the midpoint of segment DM. Point X is the reflection of point N across line O. Point P is the midpoint of segment NX. Find the distance between poin... | 8.79 | MATH |
[
{
"content": "Let ABCD be a square with center M and circumradius 12. Line U is the angle bisector of angle DCB. Let O be the reflection of line U through point B. Point F is the reflection of point A across point D. Let Z be the reflection of point F across point A. Let R be the line through point A perpendicu... | 8.49 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center O and circumradius 5. Line V passes through points F and O. Line R passes through points G and J. Let T be the reflection of line R across line V. Point M is the reflection of point I across line T. What is the measure of angle FDM, in radians? Expre... | 2.36 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 4. Let S be the perpendicular bisector of segment KA. Line J passes through point F perpendicular to line S. Point T is the reflection of point K across line J. Let Q be the midpoint of segment TE. What is the distance between points K and... | 5.29 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center O and circumradius 9. Let K be the angle bisector of angle CEB. Let Q be the line through point C perpendicular to line K. Point G is the reflection of point D across line Q. Point U is the midpoint of segment AE. Point V is the midpoint of segment EG. What... | 13.21 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center M and circumradius 10. Line Z passes through points E and M. Let V be the rotation of point C by angle 11pi/12 around point D. Line P passes through point H parallel to line Z. Line S is the reflection of line Z across line P. Point R is the refl... | 18.84 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center S and circumradius 11. Let V be the midpoint of segment EB. Point O is the midpoint of segment EV. Point X is the reflection of point F across segment SO. What is the length of segment XB? Express your answer as a decimal number rounded to 2 decimal p... | 6.26 | MATH |
[
{
"content": "Let ACDE be a square with center B and circumradius 4. Let G be the reflection of point B across point E. Line U is the perpendicular bisector of segment EB. Line Z is the reflection of line U across point G. Point X is the reflection of point D across line Z. Point T is the reflection of point X ... | 50.91 | MATH |
[
{
"content": "ABCDEFGIJKLM is a regular dodecagon with center H and circumradius 6. Let Y be the circumcircle of polygon ABCDEFGIJKLM. Line S passes through points K and A. Let N be the reflection of circle Y through point M. Let V be the line through points G and M. Lines S and V intersect at point W. Let X be... | 5.38 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center P and circumradius 10. Line Q is the perpendicular bisector of segment GI. Line M passes through point F parallel to line Q. Point T is the reflection of point G across point F. Point V is the reflection of point T across line M. What is the measure of an... | 0.63 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Q and circumradius 2. Let M be the rotation of point Q by angle 3pi/4 around point B. Let P be the angle bisector of angle GMD. Let V be the line through points F and E. Let K be the reflection of line P through point H. Line U is the reflection of lin... | 9.3 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center I and circumradius 8. Line U passes through points G and C. Let W be the line through point A perpendicular to line U. Point Y is the reflection of point B across line W. Point H is the reflection of point Y across line U. Let O be the midpoint of segment... | 11.74 | MATH |
[
{
"content": "Let ABCE be a square with center D and circumradius 7. Point K is the reflection of point E across point B. Let U be the circumcircle of polygon ABCE. Let S be the inversion of point K in circle U. Point V is the midpoint of segment KD. Find the distance between points S and V. Express your answer... | 8.17 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center U and circumradius 9. Line K passes through points C and A. Line Z passes through point E parallel to line K. Line N passes through point U parallel to line K. Let M be the reflection of line N across line Z. Point I is the reflection of point F across line ... | 36.0 | MATH |
[
{
"content": "Let ABCDFGHIJKLM be a regular dodecagon with center E and circumradius 6. Let Z be the line through points C and F. Let N be the reflection of line Z through point A. Point S is the intersection of segment EK and line N. What is the length of segment AS? Express your answer as a decimal number rou... | 7.94 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center Q and circumradius 8. Let N be the reflection of point Q across point H. Let M be the reflection of point I across point E. Point U is the midpoint of segment NH. What is the distance between points U and M? Express your answer as a decimal number rou... | 30.74 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center K and circumradius 8. Line W passes through points I and D. Point J is the intersection of segment AG and line W. Let V be the midpoint of segment AG. What is the measure of angle IJV, in radians? Express your answer as a decimal number rounded to 2 dec... | 1.75 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center U and circumradius 3. Line O is the angle bisector of angle FHA. Line X passes through point K parallel to line O. Line X and segment LB intersect at point M. Find the length of segment UM. Express your answer as a decimal number rounded to 2 decimal... | 2.85 | MATH |
[
{
"content": "ABCDEFH is a regular 7-gon with center G and circumradius 3. Let U be the circumcircle of polygon ABCDEFH. Let Y be the reflection of circle U through point A. Let J be the inversion of point H in circle Y. Let I be the reflection of point J across point H. Find the length of segment EI. Express y... | 3.22 | MATH |
[
{
"content": "Let ET = 1. ABCDFG is a regular hexagon with center T and circumradius 3. Let Q be the perpendicular bisector of segment BT. Point Z is the intersection of segments DG and FB. Point W is the reflection of point Z across line Q. What is the length of segment WC? Express your answer as a decimal num... | 3.97 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center L and circumradius 9. Let Z be the circumcircle of polygon ABCDEF. Let Y be the line through points B and L. Circle K is the reflection of circle Z across point F. Let U be the reflection of circle K across line Y. Point Q is the inversion of point B with re... | 26.28 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center X and circumradius 5. Line U is the angle bisector of angle FIA. Line Z passes through point X parallel to line U. Let O be the reflection of line Z across line U. Line O and segment EA intersect at point V. What is the measure of angle HAV, in radians? Exp... | 1.05 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center U and circumradius 5. Point K is obtained by rotating point B by angle pi/3 about point A. Line S passes through points E and G. Let I be the perpendicular bisector of segment KH. Line Q is the reflection of line S across point A. Let Y be the reflection o... | 20.14 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center Z and circumradius 2. Let Y be the line through points I and A. Line N is the reflection of line Y across point H. Point L is the reflection of point A across line N. Let P be the angle bisector of angle FEJ. Let R be the midpoint of segment LK. Poin... | 3.21 | MATH |
[
{
"content": "Let ABCD be a square with center O and circumradius 3. Point L is the midpoint of segment DC. Let W be the circumcircle of polygon ABCD. Circle E is the reflection of circle W across point D. Let J be the inversion of point O in circle E. Point I is the reflection of point B across point L. Find t... | 3.35 | MATH |
[
{
"content": "Let ABCDEFGHIKL be a regular 11-gon with center J and circumradius 10. Let R be the midpoint of segment LG. Point O is the midpoint of segment RL. Let P be the midpoint of segment GO. Find the distance between points P and J. Express your answer as a decimal number rounded to 2 decimal places.\n\n... | 4.74 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center U and circumradius 3. Let J be the midpoint of segment CA. Let W be the midpoint of segment AU. Line X is the angle bisector of angle JCW. Point M is the reflection of point D across line X. Point Z is the midpoint of segment FM. Find the length of seg... | 3.56 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center J and circumradius 1. Let L be the circumcircle of polygon ABCDEF. Line Y is the angle bisector of angle AFC. Let G be the midpoint of segment BD. Let M be the reflection of circle L through point F. Point T is the midpoint of segment CG. Circle X is the ref... | 2.26 | MATH |
[
{
"content": "Let ACDEFG be a regular hexagon with center B and circumradius 8. Let K be the perpendicular bisector of segment FE. Let Z be the line through point D parallel to line K. Let R be the reflection of line Z across line K. Point Q is the reflection of point D across line R. What is the distance betwe... | 21.17 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center M and circumradius 7. Line T is the angle bisector of angle DGF. Point J is the reflection of point D across line T. Line X is the perpendicular bisector of segment JF. Point N is the reflection of point D across point B. Line L passes through point H ... | 12.93 | MATH |
[
{
"content": "ABCDFGHI is a regular octagon with center E and circumradius 11. Let V be the circumcircle of polygon ABCDFGHI. Line P passes through points I and C. Circle J is the reflection of circle V across line P. Point U is the inversion of point B with respect to circle J. What is the distance between poi... | 20.33 | MATH |
[
{
"content": "ABCDEFGHJKLM is a regular dodecagon with center I and circumradius 4. Let O be the line through point K parallel to segment BE. Let R be the midpoint of segment BE. Point N is the reflection of point E across line O. Find the distance between points N and R. Express your answer as a decimal number... | 13.68 | MATH |
[
{
"content": "Let ABCEFGHI be a regular octagon with center D and circumradius 10. Let W be the circumcircle of polygon ABCEFGHI. Let Z be the angle bisector of angle FED. Circle M is the reflection of circle W across point I. Point R is the reflection of point D across point C. Let Y be the inversion of point ... | 48.81 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center O and circumradius 10. Let S be the reflection of point G across point A. Let N be the angle bisector of angle OFB. Let J be the line through points A and B. Let T be the line through point E perpendicular to line N. Let K be the reflection of line J acros... | 44.34 | MATH |
[
{
"content": "Let ABDEFG be a regular hexagon with center C and circumradius 11. Let Y be the midpoint of segment EF. Point R is the midpoint of segment BY. Let H be the line through points R and A. Point V is the reflection of point D across line H. What is the distance between points V and A? Express your ans... | 19.05 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center W and circumradius 3. Point T is the reflection of point A across point B. Let Q be the line through points E and W. Point X is the reflection of point T across line Q. Let U be the midpoint of segment WD. Find the distance between points U and X. Express your ... | 6.29 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center H and circumradius 11. Let J be the line through points H and D. Let O be the line through point H perpendicular to line J. Point U is the midpoint of segment EA. Line Z is the reflection of line O across point B. Let M be the line through point D parallel to... | 23.6 | MATH |
[
{
"content": "Let ABCD be a square with center X and circumradius 12. Point Z is the reflection of point X across segment DA. Let U be the line through points B and C. Point O is the reflection of point Z across line U. Find the distance between points Z and O. Express your answer as a decimal number rounded to... | 50.91 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center X and circumradius 11. Let Z be the circumcircle of polygon ABCDEFGH. Let R be the reflection of circle Z through point H. Line I passes through points X and F. Circle O is the reflection of circle R across line I. Let P be the inversion of point E in circ... | 17.14 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center X and circumradius 7. Let U be the perpendicular bisector of segment HE. Let O be the line through points J and D. Line T is the reflection of line O across line U. Let W be the line through point D perpendicular to line T. Point Z is the reflection of po... | 13.31 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center U and circumradius 12. Point S is the midpoint of segment BE. Let P be the circumcircle of polygon ABCDEFG. Let T be the reflection of circle P through point F. Let J be the angle bisector of angle UGS. Line K is the reflection of line J across point D. Let W... | 57.02 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center L and circumradius 6. Point V is the midpoint of segment AC. Let P be the midpoint of segment VD. Point J is the reflection of point F across segment AP. Find the length of segment BJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nP... | 1.87 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center T and circumradius 8. Line R passes through points A and C. Line X passes through point D parallel to line R. Let O be the perpendicular bisector of segment FA. Let U be the reflection of line O across line X. Lines X and U intersect at point W. Find... | 0.79 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center S and circumradius 11. Let P be the angle bisector of angle CFD. Line Y is the reflection of line P across point H. Line K passes through point A perpendicular to line Y. Line T passes through point D perpendicular to line K. Let W be the reflection o... | 17.85 | MATH |
[
{
"content": "Let ABCDEFGHJK be a regular 10-gon with center I and circumradius 6. Point X is the midpoint of segment CG. Point P is the reflection of point X across segment BD. Point M is the midpoint of segment BD. Point U is the midpoint of segment DM. What is the distance between points U and P? Express you... | 4.28 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center M and circumradius 1. Let O be the circumcircle of polygon ABCDEFG. Circle I is the reflection of circle O across point E. Point Q is the inversion of point G with respect to circle I. Let V be the reflection of point Q across point F. What is the length of s... | 1.96 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center V and circumradius 9. Z is placed 2 units away from K. Line R is the angle bisector of angle ZKC. Point P is the midpoint of segment CK. Line X passes through point C perpendicular to line R. Point M is the midpoint of segment DP. Point S is the ... | 3.99 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.