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 Z and circumradius 2. Segments AC and BI intersect at point Q. Point U is the reflection of point D across segment BI. Find the distance between points Q and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the a... | 1.95 | MATH |
[
{
"content": "Let ACDEFGHIJKLM be a regular dodecagon with center B and circumradius 5. Point S is the midpoint of segment AD. Point N is the midpoint of segment LH. What is the distance between points N and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex f... | 6.61 | MATH |
[
{
"content": "Let ABCDEGHIJKLM be a regular dodecagon with center F and circumradius 9. Let R be the angle bisector of angle FAH. Let X be the reflection of point F across point L. Line V is the perpendicular bisector of segment XM. Let Z be the reflection of line V across line R. Point P is the reflection of p... | 21.06 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Z and circumradius 6. Point V is the reflection of point A across point I. Let T be the perpendicular bisector of segment EF. Let Y be the circumcircle of polygon ABCDEFGHIJKL. Let Q be the inversion of point V in circle Y. Line M passes through ... | 13.04 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center L and circumradius 10. Let O be the rotation of point B by angle pi around point E. Let Y be the rotation of point O by angle 3pi/4 around point C. Line J passes through point Y parallel to segment LA. Point K is the reflection of point O across segment LA.... | 10.49 | MATH |
[
{
"content": "ABCDEFGIJ is a regular 9-gon with center H and circumradius 11. Let X be the line through points E and C. Let L be the reflection of line X through point I. Point O is the reflection of point G across line L. Point R is the midpoint of segment HA. Find the length of segment OR. Express your answer... | 51.95 | MATH |
[
{
"content": "ABCEF is a regular 5-gon with center D and circumradius 3. Point P is the reflection of point F across segment AB. Let Y be the reflection of point F across point D. Point W is the reflection of point Y across segment AB. What is the measure of angle WPA, in radians? Express your answer as a decim... | 0.94 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center I and circumradius 6. Line W passes through points D and B. Point Z is the reflection of point G across line W. Point T is the midpoint of segment FA. Point L is the reflection of point Z across point A. Find the length of segment TL. Express your answer as a... | 14.3 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center V and circumradius 3. Let Z be the line through points H and G. Point P is the midpoint of segment AV. Line M passes through point F perpendicular to line Z. Point S is the reflection of point I across line M. Let U be the line through points S and F. Poi... | 2.65 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 6. Let T be the angle bisector of angle CBO. Let K be the circumcircle of polygon ABCDEF. Line I passes through point E perpendicular to line T. Let U be the reflection of circle K through point A. Let P be the inversion of point O in circ... | 8.14 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center R and circumradius 1. Point Q is the reflection of point D across segment CB. Point I is the reflection of point G across segment CB. Point T is the reflection of point I across point H. Find the length of segment TQ. Express your answer as a decimal numbe... | 5.54 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center V and circumradius 8. Point H is the midpoint of segment BV. Let I be the angle bisector of angle CAV. Point Q is the midpoint of segment HV. Line N is the reflection of line I across point V. Line J passes through points Q and E. Point O is the intersectio... | 5.27 | MATH |
[
{
"content": "ABDEFGHI is a regular octagon with center C and circumradius 2. Line U is the angle bisector of angle FGE. Line S is the perpendicular bisector of segment ID. Let X be the reflection of line U across line S. Point Q is the reflection of point A across line X. What is the measure of angle QFB, in r... | 2.36 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Y and circumradius 4. Let W be the midpoint of segment CY. Point J is the midpoint of segment HW. Point N is the midpoint of segment JA. Let P be the midpoint of segment JN. Let I be the reflection of point F across point P. What is the distance between po... | 7.18 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center S and circumradius 9. Let M be the angle bisector of angle KSC. Let V be the line through point S perpendicular to line M. Let Q be the reflection of point J across point F. Let Z be the reflection of line V through point Q. Point N is the reflection... | 38.43 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center K and circumradius 2. Point Z is the reflection of point B across point D. Let Q be the midpoint of segment BC. Point U is the reflection of point H across point C. Point T is the reflection of point U across segment CZ. Find the length of segment QT. Exp... | 3.73 | MATH |
[
{
"content": "Let ABCDEFGHIKLM be a regular dodecagon with center J and circumradius 5. Let Y be the angle bisector of angle DMB. Line S passes through point L perpendicular to line Y. Point T is the reflection of point J across point I. Point O is the reflection of point D across line S. Point V is the reflect... | 19.36 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center Y and circumradius 6. Let Q be the midpoint of segment BA. Let N be the reflection of point G across point I. Line L is the angle bisector of angle GYA. Let U be the reflection of line L through point Q. Let S be the reflection of line U through point I. ... | 21.08 | MATH |
[
{
"content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 5. Line W passes through point A perpendicular to segment GJ. Line R is the reflection of line W across point K. Point S is the reflection of point A across line R. What is the length of segment SH? Express your answer as a decimal... | 19.32 | MATH |
[
{
"content": "Let ABCEF be a regular 5-gon with center D and circumradius 7. Let G be the reflection of point E across point F. Let L be the circumcircle of polygon ABCEF. Circle O is the reflection of circle L across point A. Point T is the midpoint of segment EC. Let K be the inversion of point G in circle O.... | 18.27 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center V and circumradius 8. Line I is the angle bisector of angle GAB. Point R is the reflection of point E across point F. Let S be the reflection of point R across point G. Point J is the reflection of point S across line I. What is the distance between points... | 0.5 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center L and circumradius 2. Line W is the angle bisector of angle KDE. Line M passes through points J and G. Let Q be the reflection of line W across line M. Lines Q and M intersect at point P. Find the distance between points B and P. Express your answer as a... | 3.46 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center P and circumradius 5. Point Y is obtained by rotating point F by angle pi/2 about point L. Point R is the reflection of point Y across point A. Line V is the perpendicular bisector of segment FL. Let N be the line through point P perpendicular to... | 10.73 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center X and circumradius 11. Point Q is the midpoint of segment CF. Let H be the midpoint of segment XG. Point T is the midpoint of segment DQ. Let Z be the angle bisector of angle FAT. Line J passes through point H perpendicular to line Z. Point S is the refle... | 17.83 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center R and circumradius 3. Let V be the midpoint of segment BC. Point N is the reflection of point V across segment GE. Point J is the midpoint of segment CN. Find the distance between points R and J. Express your answer as a decimal number rounded to 2 dec... | 2.83 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center M and circumradius 5. Line S is the perpendicular bisector of segment MG. Line Z passes through point D perpendicular to segment CE. Line Y passes through point F perpendicular to segment CE. Line X passes through point I parallel to line Z. Line L passe... | 50.35 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center W and circumradius 7. Let Z be the perpendicular bisector of segment FB. Let V be the line through point D parallel to segment EA. Let K be the reflection of line Z through point F. Lines V and K intersect at point P. Let L be the midpoint of segment A... | 15.69 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center I and circumradius 1. Point V is the reflection of point E across point I. Let L be the line through points V and A. Point N is the reflection of point I across line L. Let F be the midpoint of segment NI. What is the length of segment EF? Express your answ... | 1.43 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center M and circumradius 2. Let S be the rotation of point E by angle 7pi/12 around point B. Let G be the perpendicular bisector of segment AC. Point K is the midpoint of segment AM. Line L is the reflection of line G across point C. Point T is the reflection ... | 2.07 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center S and circumradius 3. Let I be the reflection of point E across point D. Line Z is the perpendicular bisector of segment BD. Point H is the reflection of point I across line Z. Let G be the reflection of point H across point A. What is the length of segm... | 6.0 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center X and circumradius 9. Let W be the line through points B and E. Line M is the angle bisector of angle BHD. Line Q passes through point A parallel to line W. Point V is the intersection of line Q and segment DG. Let O be the line through point F perpendicula... | 1.75 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center M and circumradius 8. Point F is the midpoint of segment EC. Point U is the reflection of point F across point B. Let L be the midpoint of segment UA. Find the length of segment LC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPre... | 14.41 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center X and circumradius 9. Point Y is the midpoint of segment FH. Let T be the angle bisector of angle IKJ. Line P passes through point A perpendicular to line T. Point S is the reflection of point I across line P. What is the length of segment SY? Expres... | 32.11 | MATH |
[
{
"content": "ABCDEFGHJKLM is a regular dodecagon with center I and circumradius 9. Point W is the midpoint of segment AI. Let P be the reflection of point E across point G. Point O is the reflection of point B across point W. What is the distance between points O and P? Express your answer as a decimal number ... | 15.07 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Z and circumradius 8. Let Q be the reflection of point G across point A. Let V be the midpoint of segment DQ. Let U be the reflection of point Z across point Q. Find the length of segment VU. Express your answer as a decimal number rounded to 2 decimal pla... | 28.35 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center S and circumradius 3. Let V be the perpendicular bisector of segment FC. Line T is the reflection of line V across point L. Point M is the reflection of point L across line T. Line N passes through point M parallel to line T. Point R is the reflectio... | 12.3 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Z and circumradius 7. Let X be the rotation of point I by angle pi/4 around point D. Let W be the line through point Z parallel to segment DB. Let S be the line through point D perpendicular to line W. Point N is the reflection of point X across line... | 21.68 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center O and circumradius 5. Point U is the reflection of point O across point J. Line P passes through point D perpendicular to segment HE. Line Q passes through point U parallel to segment HE. Line N passes through point G parallel to line P. Point Y is t... | 3.39 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Y and circumradius 1. Line P passes through point G perpendicular to segment LH. Let O be the reflection of line P through point L. Let Z be the reflection of line O across line P. Point W is the reflection of point A across line Z. What is the dista... | 10.46 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center X and circumradius 1. Let T be the angle bisector of angle XDC. Let L be the line through point A perpendicular to line T. Line G is the reflection of line L across point E. Let W be the line through point E perpendicular to line G. Point F is the reflectio... | 2.69 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center X and circumradius 12. Let N be the line through points C and X. Let P be the line through point B parallel to line N. Let S be the reflection of point I across point C. Point Q is the intersection of line P and segment JG. Find the length of segment ... | 41.32 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Y and circumradius 8. Line T is the angle bisector of angle YAJ. Point N is the reflection of point L across line T. Let M be the reflection of point G across point H. Point Q is the reflection of point M across line T. What is the distance between p... | 13.4 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 2. Point I is the reflection of point F across point B. Let J be the rotation of point E by angle pi/2 around point C. Line S is the angle bisector of angle BDJ. Let W be the midpoint of segment FA. Point T is the reflection of point W across... | 10.31 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Y and circumradius 10. Let M be the rotation of point D by angle 3pi/4 around point A. Let N be the circumcircle of polygon ABCDEF. Let S be the line through point M perpendicular to segment DA. Let I be the reflection of circle N across line S. Point K is t... | 51.72 | MATH |
[
{
"content": "Let ABCDFG be a regular hexagon with center E and circumradius 4. Let Z be the rotation of point B by angle pi/4 around point E. Point I is the midpoint of segment FC. Let T be the line through points E and Z. Point X is on line T. Line L passes through points I and X. Point R is the reflection of... | 3.98 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center P and circumradius 12. Point J is the midpoint of segment HF. Let L be the midpoint of segment IJ. Point W is the reflection of point L across segment GB. What is the length of segment WP? Express your answer as a decimal number rounded to 2 decimal places.... | 5.24 | MATH |
[
{
"content": "Let ACDEFGHI be a regular octagon with center B and circumradius 5. Line T is the angle bisector of angle CEF. Let P be the midpoint of segment HI. Let M be the angle bisector of angle IBE. Point X is the reflection of point P across line M. Let N be the midpoint of segment PG. Let J be the line t... | 4.01 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center K and circumradius 6. Let Q be the line through point K parallel to segment EF. Line T passes through points B and D. Lines T and Q intersect at point M. Point U is the reflection of point D across segment EF. Find the length of segment UM. Express your a... | 9.54 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center Z and circumradius 2. Let U be the perpendicular bisector of segment ZC. Let S be the line through point A parallel to line U. Segment DH and line S intersect at point M. Point T is the reflection of point Z across segment DH. What is the distance betwe... | 0.69 | MATH |
[
{
"content": "ABCDEGHIJKLM is a regular dodecagon with center F and circumradius 3. Let N be the reflection of point F across point G. Let O be the line through points N and E. Let Q be the line through point H parallel to line O. Point R is the reflection of point C across line Q. Let S be the midpoint of segm... | 4.69 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center V and circumradius 3. Let K be the reflection of point C across point G. Point N is the reflection of point F across point K. Let L be the midpoint of segment HA. Line S passes through points L and N. Point I is the reflection of point E across line S. Wha... | 10.45 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center P and circumradius 7. Let X be the circumcircle of polygon ABCDEFGHIJKL. Let V be the reflection of circle X through point G. Let T be the reflection of point C across point J. Let U be the reflection of circle V through point C. Point M is the inver... | 27.21 | MATH |
[
{
"content": "Let ABCDFGHIJK be a regular 10-gon with center E and circumradius 10. Line L passes through points K and G. Let Z be the line through point F parallel to line L. Point W is the reflection of point B across line Z. Let S be the midpoint of segment ID. What is the length of segment WS? Express your ... | 8.87 | MATH |
[
{
"content": "ACDEFGHIJKLM is a regular dodecagon with center B and circumradius 11. Let Z be the circumcircle of polygon ACDEFGHIJKLM. Point N is the midpoint of segment AJ. Point P is the inversion of point N with respect to circle Z. What is the distance between points L and P? Express your answer as a decim... | 11.0 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Y and circumradius 6. Let Z be the rotation of point B by angle pi around point C. Let T be the perpendicular bisector of segment BA. Point V is the reflection of point Z across line T. Point N is the reflection of point V across segment BE. Point J is the... | 4.92 | MATH |
[
{
"content": "ABCDEGHIJKL is a regular 11-gon with center F and circumradius 12. Let V be the circumcircle of polygon ABCDEGHIJKL. Let W be the midpoint of segment AE. Let P be the reflection of circle V through point A. Point Z is the reflection of point F across segment AE. Point S is the inversion of point W... | 15.63 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center L and circumradius 3. Let Y be the line through point B perpendicular to segment GH. Let P be the line through point E parallel to line Y. Point X is the reflection of point G across line P. Point J is the reflection of point D across segment GH. Find the ... | 6.42 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Y and circumradius 3. Line G is the angle bisector of angle ACY. Let Z be the reflection of point E across point B. Let V be the line through point Z parallel to line G. Line H passes through point D parallel to line V. Point X is the reflection of point... | 8.2 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 5. Let U be the circumcircle of polygon ABCDEFGH. Let Z be the reflection of circle U through point A. Let O be the perpendicular bisector of segment HE. Point V is the midpoint of segment HA. Point S is the inversion of point V with... | 5.35 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Z and circumradius 4. Let J be the angle bisector of angle HEZ. Point S is the reflection of point D across line J. Let W be the circumcircle of polygon ABCDEFGH. Let U be the inversion of point S in circle W. What is the length of segment HU? Express ... | 5.43 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center L and circumradius 5. Let H be the circumcircle of polygon ABCDEF. Point O is obtained by rotating point B by angle pi/12 about point F. Line R is the perpendicular bisector of segment OB. Point U is the reflection of point L across line R. Let V be the line... | 3.72 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Q and circumradius 1. Let P be the perpendicular bisector of segment AB. Let L be the line through point E parallel to line P. Let U be the reflection of line L across line P. Let S be the line through point D perpendicular to segment BQ. Point Y is the re... | 3.46 | MATH |
[
{
"content": "Let ABCDFGHIJK be a regular 10-gon with center E and circumradius 9. Let L be the angle bisector of angle DFJ. Line X is the reflection of line L across point B. Point V is the reflection of point J across line X. Let W be the reflection of point V across point A. Find the length of segment WG. Ex... | 30.89 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center Y and circumradius 5. Line K passes through points A and J. Point N is obtained by rotating point E by angle pi/12 about point H. Line Z is the angle bisector of angle BFN. Line M is the reflection of line K across line Z. Line P passes through point ... | 36.95 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center V and circumradius 1. Let M be the line through point J perpendicular to segment IC. Line Z is the reflection of line M across point L. Let Y be the line through point G parallel to line Z. Line Y and segment IC intersect at point R. What is the dist... | 1.45 | MATH |
[
{
"content": "Let ABCDEFGHIJKM be a regular dodecagon with center L and circumradius 9. Line P is the perpendicular bisector of segment JE. Let U be the perpendicular bisector of segment LB. Let T be the reflection of line U across line P. Line W is the reflection of line P across line T. Point X is the interse... | 11.15 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 6. Line V is the perpendicular bisector of segment EF. Let O be the reflection of line V through point H. Line M passes through point C perpendicular to line O. Point Q is the reflection of point E across line M. Find the length of s... | 4.59 | MATH |
[
{
"content": "Let ABCDFGHIJKLM be a regular dodecagon with center E and circumradius 1. Let Z be the reflection of point F across point D. Let V be the perpendicular bisector of segment LZ. Let P be the line through point G perpendicular to line V. Point R is the reflection of point M across line P. Point N is ... | 3.61 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center N and circumradius 12. Line O is the angle bisector of angle CFE. Let T be the line through point A perpendicular to line O. Let M be the circumcircle of polygon ABCDEF. Let R be the reflection of circle M across line T. Let V be the inversion of point C in ... | 7.86 | MATH |
[
{
"content": "Let ABCD be a square with center G and circumradius 2. Line Q is the perpendicular bisector of segment DC. Let F be the line through point D perpendicular to line Q. Point H is the reflection of point A across line F. Point E is the reflection of point H across point G. Let L be the midpoint of se... | 5.83 | MATH |
[
{
"content": "ABDEFGHI is a regular octagon with center C and circumradius 4. Line X passes through points G and E. Let Y be the reflection of line X through point B. Let Z be the reflection of line Y through point H. Point T is the reflection of point B across line Z. Find the distance between points T and I. ... | 23.32 | MATH |
[
{
"content": "Let ABCDEFGHJKLM be a regular dodecagon with center I and circumradius 12. Let X be the line through points F and H. Line V passes through point E parallel to line X. Point Y is the intersection of line V and segment AG. What is the length of segment DY? Express your answer as a decimal number rou... | 13.42 | MATH |
[
{
"content": "ABCE is a square with center D and circumradius 12. Let F be the midpoint of segment AE. Let H be the reflection of point D across point F. Line R passes through point A perpendicular to segment CH. Point L is the reflection of point F across line R. Find the measure of angle LFB, in radians. Expr... | 2.36 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center Q and circumradius 4. Line O passes through points K and J. Point U is the reflection of point F across line O. Let P be the midpoint of segment DK. Find the length of segment UP. Express your answer as a decimal number rounded to 2 decimal places.\n... | 11.46 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center P and circumradius 7. Let R be the circumcircle of polygon ABCDEFGHIJKL. Let Q be the midpoint of segment IK. Point M is the inversion of point Q with respect to circle R. Let T be the midpoint of segment MH. Find the distance between points I and T.... | 0.54 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center M and circumradius 1. Let W be the midpoint of segment AM. Line O is the angle bisector of angle DEB. Line Q is the reflection of line O across point A. Point Y is the reflection of point B across line Q. Let T be the midpoint of segment YE. Let X be the reflec... | 1.84 | MATH |
[
{
"content": "Let ABCDEG be a regular hexagon with center F and circumradius 6. Let K be the angle bisector of angle GFD. Point Z is the reflection of point F across point G. Point M is the midpoint of segment ZE. Point P is the reflection of point Z across line K. What is the length of segment PM? Express your... | 15.59 | MATH |
[
{
"content": "Let ABCDFG be a regular hexagon with center E and circumradius 3. Point S is the reflection of point D across point B. Let P be the circumcircle of polygon ABCDFG. Let T be the reflection of circle P through point S. Let Y be the reflection of circle T through point E. Point J is the inversion of ... | 12.58 | MATH |
[
{
"content": "ACDEFGHIJKL is a regular 11-gon with center B and circumradius 7. Line V is the angle bisector of angle HBK. Line W passes through point C parallel to segment AK. Line M is the reflection of line V across line W. Point P is the intersection of segment AK and line M. Find the length of segment PB. ... | 5.91 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center M and circumradius 4. Let Y be the angle bisector of angle BMG. Line Z passes through points F and H. Line K is the reflection of line Y across line Z. Point N is the reflection of point M across line K. What is the length of segment NE? Express your a... | 12.54 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center X and circumradius 9. Let W be the circumcircle of polygon ABCDE. Point V is the midpoint of segment BC. Let Z be the line through points C and V. Let Y be the reflection of circle W across line Z. Let H be the inversion of point E in circle Y. Find the measure... | 1.89 | MATH |
[
{
"content": "Let ABCDEFHIJK be a regular 10-gon with center G and circumradius 5. Let W be the circumcircle of polygon ABCDEFHIJK. Point X is the midpoint of segment GI. Circle M is the reflection of circle W across point C. Let R be the inversion of point E in circle M. Let U be the midpoint of segment JX. Wh... | 11.36 | MATH |
[
{
"content": "QV = 11. Let ABCDEFG be a regular 7-gon with center V and circumradius 1. Let U be the midpoint of segment FA. Point S is the reflection of point G across point A. Point R is the reflection of point S across segment DA. Find the distance between points R and U. Express your answer as a decimal num... | 0.72 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Q and circumradius 11. Line H is the angle bisector of angle EAD. Point R is the reflection of point C across line H. Line N is the angle bisector of angle REA. Line S is the reflection of line N across line H. Line M passes through point Q parallel to line ... | 31.84 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center X and circumradius 12. Point G is the midpoint of segment CD. Let M be the line through point C perpendicular to segment EC. Point P is the reflection of point G across line M. Point Y is the reflection of point E across segment PG. What is the length of... | 15.87 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center N and circumradius 1. Let T be the midpoint of segment JL. Let M be the midpoint of segment DN. Line U is the angle bisector of angle MHE. Point Q is the reflection of point T across line U. Point O is the reflection of point I across point H. What i... | 0.81 | MATH |
[
{
"content": "Let ABCDEFHI be a regular octagon with center G and circumradius 1. Let T be the midpoint of segment BE. Line Z is the perpendicular bisector of segment GD. Point W is the reflection of point B across line Z. Let Q be the reflection of point T across point W. Point O is the midpoint of segment CB.... | 1.63 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center V and circumradius 8. Let Q be the angle bisector of angle EVH. Let K be the reflection of point V across point B. Point T is the reflection of point C across point K. Let L be the reflection of line Q through point D. Point J is the reflection of point... | 44.87 | MATH |
[
{
"content": "Let ABDE be a square with center C and circumradius 2. Let H be the line through points C and D. Let N be the circumcircle of polygon ABDE. Let F be the angle bisector of angle DEB. Line S is the reflection of line F across line H. Circle L is the reflection of circle N across line S. Point K is t... | 1.77 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center H and circumradius 12. Let L be the reflection of point C across point H. Let Y be the circumcircle of polygon ABCDE. Line R is the perpendicular bisector of segment CH. Let J be the reflection of line R through point C. Circle I is the reflection of circle... | 23.06 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center X and circumradius 5. Point F is obtained by rotating point X by angle pi about point C. Let R be the perpendicular bisector of segment BD. Let Q be the line through points F and A. Line N is the reflection of line Q across line R. Point U is the reflection of ... | 8.79 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center P and circumradius 4. Point V is the reflection of point E across point H. Line I is the perpendicular bisector of segment CB. Let Z be the line through point D parallel to line I. Point Y is the reflection of point V across line Z. What is the distanc... | 20.13 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center V and circumradius 3. Line Z passes through points V and G. Let S be the line through points H and A. Line X passes through point F parallel to line Z. Lines S and X intersect at point J. Let O be the midpoint of segment BH. Find the length of segment OJ. ... | 13.07 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center V and circumradius 8. Let H be the angle bisector of angle EBD. Let J be the line through point A perpendicular to line H. Point N is the reflection of point D across line J. Let O be the reflection of point D across point N. What is the length of segment C... | 26.99 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center N and circumradius 1. Let X be the midpoint of segment HD. Let Z be the midpoint of segment XG. Let U be the angle bisector of angle NDZ. Line S is the reflection of line U across point Z. Point M is the midpoint of segment DX. Let R be the line ... | 1.32 | MATH |
[
{
"content": "Let ABCDF be a regular 5-gon with center E and circumradius 1. Line T passes through points A and D. Point O is obtained by rotating point C by angle 3pi/4 about point D. Let Y be the perpendicular bisector of segment OA. Line G passes through point B parallel to line Y. Point S is the intersectio... | 1.05 | MATH |
[
{
"content": "ABCD is a square with center N and circumradius 10. Point J is the midpoint of segment CD. Point W is the reflection of point J across segment CB. Let Z be the line through points A and W. Point Q is the reflection of point C across line Z. Find the distance between points Q and D. Express your an... | 19.61 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center O and circumradius 11. Point R is the reflection of point G across point E. Let Q be the line through points C and R. Point W is the reflection of point A across line Q. Point S is the midpoint of segment WH. What is the length of segment SC? Express y... | 10.16 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center H and circumradius 8. Point R is the midpoint of segment CH. Line G is the angle bisector of angle BCR. Point N is the reflection of point R across line G. Let Q be the midpoint of segment HR. Point J is the midpoint of segment RC. Let K be the midpoint of segm... | 10.39 | MATH |
[
{
"content": "ABCE is a square with center D and circumradius 2. Line N is the perpendicular bisector of segment ED. Let Q be the reflection of line N through point E. Point X is the reflection of point E across point A. Let O be the perpendicular bisector of segment BC. Let G be the reflection of line Q across... | 2.24 | MATH |
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