messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "MF = 11. Let Z be the midpoint of segment FM. Point E is the reflection of point Z across point F. Let I be the rotation of point F by angle 11pi/12 around point Z. Line P is the perpendicular bisector of segment IE. Point G is the midpoint of segment MI. Let B be the midpoint of segment IZ. Let S... | 13.06 | MATH |
[
{
"content": "HK = 6. Point L is the midpoint of segment KH. Let U be the perpendicular bisector of segment LH. Let Z be the midpoint of segment LH. Point M is the reflection of point Z across point H. Point X is the midpoint of segment LZ. Point W is the reflection of point X across line U. Find the distance b... | 2.25 | MATH |
[
{
"content": "Let QN = 12. Point H is the midpoint of segment QN. Let T be the rotation of point H by angle pi/2 around point Q. Let Y be the angle bisector of angle TNQ. Point D is on line Y with |DN| = 9. Point E is the reflection of point N across segment TQ. Let L be the reflection of point D across point H... | 18.0 | MATH |
[
{
"content": "BV = 3. Point S is the reflection of point V across point B. Let F be the rotation of point B by angle pi/2 around point S. Line R passes through point F perpendicular to segment FV. Point C is the reflection of point V across point S. Point H is the reflection of point C across line R. Let P be t... | 3.42 | MATH |
[
{
"content": "Let YI = 1. Let M be the midpoint of segment IY. Let J be the rotation of point M by angle 7pi/12 around point I. Point Z is the midpoint of segment JM. Let G be the reflection of point I across point Z. Point U is the midpoint of segment ZG. Point D is the midpoint of segment GM. Let B be the ref... | 0.36 | MATH |
[
{
"content": "HX = 11. Line N is the perpendicular bisector of segment XH. Line Y is the reflection of line N across point X. Point W is the midpoint of segment XH. Let T be the midpoint of segment XW. Point O is the reflection of point H across point T. Point J is the midpoint of segment XO. Point E is the ref... | 13.75 | MATH |
[
{
"content": "Let XC = 11. Let K be the line through points X and C. Point Y is on line K with |YX| = 1. Line E is the perpendicular bisector of segment CX. Point U lies on line E at distance 2 from point C. Let R be the midpoint of segment XY. Let S be the reflection of point U across point R. Point A is the m... | 2.0 | MATH |
[
{
"content": "Let AO = 7. Let Y be the reflection of point O across point A. Let G be the midpoint of segment AY. Point T is the reflection of point G across point O. Point Z is the midpoint of segment TY. Find the distance between points Y and Z. Express your answer as a decimal number rounded to 2 decimal pla... | 12.25 | MATH |
[
{
"content": "Let MS = 6. Let R be the reflection of point S across point M. Let Q be the perpendicular bisector of segment RS. Point C is the reflection of point M across point S. Let B be the line through point C parallel to line Q. Let X be the reflection of point S across point C. Point L is obtained by rot... | 22.02 | MATH |
[
{
"content": "MW = 11. Let Z be the midpoint of segment MW. Let R be the line through point M perpendicular to segment MW. Point N is on line R with |NZ| = 9. Point H is the reflection of point N across segment MW. Line A passes through point W perpendicular to segment HW. Point L is the reflection of point N a... | 17.1 | MATH |
[
{
"content": "BC = 5. Let E be the vector from point C to point B. Let L be the midpoint of segment CB. Point F is the translation of point L by vector E. Let Y be the perpendicular bisector of segment LF. Point X lies on line Y at distance 10 from point F. Point G is the midpoint of segment CL. Line N is the a... | 3.07 | MATH |
[
{
"content": "Let IG = 7. Let Z be the rotation of point I by angle 5pi/6 around point G. Line C passes through points Z and G. Line Y passes through points Z and I. Point A lies on segment IG. Point F is the reflection of point A across line Y. Point X is the reflection of point F across line C. Find the dista... | 7.0 | MATH |
[
{
"content": "IO = 5. Let U be the rotation of point O by angle 2pi/3 around point I. Let K be the midpoint of segment UI. Line A is the perpendicular bisector of segment OI. Point H is the reflection of point K across line A. Find the distance between points H and U. Express your answer as a decimal number rou... | 9.01 | MATH |
[
{
"content": "JD = 7. Let C be the perpendicular bisector of segment DJ. Let V be the reflection of line C through point D. Point N is the reflection of point J across line V. Let Y be the midpoint of segment JD. What is the distance between points N and Y? Express your answer as a decimal number rounded to 2 d... | 17.5 | MATH |
[
{
"content": "PY = 2. Point N is obtained by rotating point P by angle pi/2 about point Y. Point Q is obtained by rotating point Y by angle pi/12 about point P. Point E is the midpoint of segment QY. Line H passes through points N and Q. Line U passes through point E perpendicular to line H. Point R is the refl... | 1.95 | MATH |
[
{
"content": "AT = 1. Point Z is obtained by rotating point A by angle 7pi/12 about point T. Point G is obtained by rotating point Z by angle 11pi/12 about point A. Point C is obtained by rotating point A by angle pi/6 about point T. Let U be the rotation of point G by angle pi/3 around point C. Let K be the ro... | 2.19 | MATH |
[
{
"content": "Let CR = 8. Point D is the reflection of point C across point R. Let Y be the rotation of point D by angle 3pi/4 around point C. Let H be the perpendicular bisector of segment CR. Line G is the reflection of line H across point R. Point W is the midpoint of segment RY. Point B is the midpoint of s... | 41.3 | MATH |
[
{
"content": "Let RN = 5. Point D is obtained by rotating point N by angle 5pi/6 about point R. Let H be the rotation of point D by angle 3pi/4 around point N. Let Z be the line through points D and H. Point P is the midpoint of segment DH. Let A be the reflection of line Z through point N. Line C passes throug... | 28.73 | MATH |
[
{
"content": "Let BL = 6. Point C is the midpoint of segment LB. Let J be the rotation of point B by angle 5pi/6 around point C. Point Q is obtained by rotating point C by angle 2pi/3 about point J. Point M is the reflection of point J across point L. Point S is the reflection of point Q across segment MB. Let ... | 7.65 | MATH |
[
{
"content": "Let JZ = 7. Let Y be the reflection of point J across point Z. Let V be the midpoint of segment ZY. Let Q be the reflection of point Y across point J. Point N is the midpoint of segment VJ. Point A is the reflection of point N across point Q. What is the distance between points A and Q? Express yo... | 19.25 | MATH |
[
{
"content": "Let QJ = 4. Point G is the midpoint of segment JQ. Point S is the midpoint of segment GQ. Let N be the rotation of point J by angle 3pi/4 around point G. Point U is the midpoint of segment NS. Line C passes through points G and N. Point R is the reflection of point U across line C. Point X is the ... | 1.77 | MATH |
[
{
"content": "XS = 1. Let J be the midpoint of segment SX. Point N is obtained by rotating point X by angle 5pi/6 about point J. Let C be the midpoint of segment JX. Let W be the midpoint of segment CN. Point G is the midpoint of segment SJ. Let K be the perpendicular bisector of segment JW. Let L be the midpoi... | 0.53 | MATH |
[
{
"content": "Let WV = 5. Let J be the perpendicular bisector of segment WV. Point U is the midpoint of segment VW. Let S be the reflection of point U across point V. Point A is the reflection of point S across line J. Point T is the midpoint of segment VS. Let O be the reflection of point A across point T. Wha... | 12.5 | MATH |
[
{
"content": "VN = 7. Point H is the midpoint of segment VN. Let B be the vector from point V to point H. Let P be the rotation of point N by angle pi/2 around point H. Let A be the midpoint of segment HV. Point Z is the translation of point N by vector B. Point R is the reflection of point A across point Z. Li... | 37.38 | MATH |
[
{
"content": "UI = 2. Point E is obtained by rotating point I by angle pi/12 about point U. Let S be the vector from point U to point E. Point K is the reflection of point I across point E. Let J be the midpoint of segment IE. Let X be the reflection of point U across point E. Point Q is obtained by rotating po... | 2.08 | MATH |
[
{
"content": "AZ = 6. Point K is the reflection of point Z across point A. Let I be the line through points A and Z. Let C be the rotation of point K by angle pi/12 around point A. Line W passes through point C perpendicular to line I. Point Y is obtained by rotating point Z by angle pi about point C. Point L i... | 24.04 | MATH |
[
{
"content": "YA = 8. Let Q be the rotation of point A by angle 7pi/12 around point Y. Let G be the reflection of point Y across point A. Line H passes through points G and Y. Let F be the line through point Q parallel to line H. Point T is the reflection of point A across line F. Let P be the midpoint of segme... | 11.64 | MATH |
[
{
"content": "Let UQ = 4. Let Y be the reflection of point Q across point U. Line J is the angle bisector of angle QUY. Point O is obtained by rotating point Y by angle 7pi/12 about point U. Let X be the reflection of point O across point Y. Let B be the reflection of line J through point X. Line V is the perpe... | 14.09 | MATH |
[
{
"content": "IU = 1. Line Z passes through points U and I. Line Q passes through point U perpendicular to line Z. Point L is the reflection of point U across point I. Point N is on line Q with |NU| = 5. Point G is the midpoint of segment LI. Line R passes through points N and L. Point S is the reflection of po... | 4.43 | MATH |
[
{
"content": "Let PS = 11. Let C be the reflection of point P across point S. Point U is obtained by rotating point C by angle 3pi/4 about point S. Point E is obtained by rotating point C by angle 5pi/12 about point P. Point A is the reflection of point P across point E. Line R is the perpendicular bisector of ... | 65.68 | MATH |
[
{
"content": "OP = 3. Point K is the midpoint of segment OP. Let T be the midpoint of segment OK. Point V is the reflection of point T across point O. Line W is the perpendicular bisector of segment VK. Let A be the reflection of line W through point K. Point Q is the reflection of point O across line A. What i... | 4.5 | MATH |
[
{
"content": "OH = 9. Let A be the midpoint of segment HO. Line S is the perpendicular bisector of segment OA. P is constructed so that HP = 9. Let R be the line through point P parallel to line S. Let J be the rotation of point A by angle pi/6 around point H. Let N be the line through point O parallel to line ... | 2.09 | MATH |
[
{
"content": "Let JL = 4. Line O is the perpendicular bisector of segment JL. Let S be the vector from point J to point L. Let M be the midpoint of segment LJ. Point N is the translation of point L by vector S. Point P is the reflection of point N across line O. Point R is obtained by rotating point L by angle ... | 16.89 | MATH |
[
{
"content": "BS = 7. Point F is the reflection of point B across point S. Let H be the rotation of point B by angle 3pi/4 around point S. Line M is the perpendicular bisector of segment BF. Let Y be the vector from point S to point B. Let L be the line through point H parallel to segment BF. Point T is obtaine... | 52.03 | MATH |
[
{
"content": "KW = 5. J is constructed so that WJ = 2. Let Z be the line through points J and W. Let R be the reflection of line Z through point K. Point P is the reflection of point J across line R. Point M is the reflection of point W across segment PK. What is the length of segment MK? Express your answer as... | 5.0 | MATH |
[
{
"content": "Let SI = 4. Let E be the rotation of point S by angle pi/6 around point I. Let G be the angle bisector of angle IES. Point C is the reflection of point S across line G. Point J is the reflection of point C across segment SI. What is the length of segment JC? Express your answer as a decimal number... | 1.93 | MATH |
[
{
"content": "Let BY = 11. Let X be the midpoint of segment YB. Let E be the midpoint of segment BX. Let R be the midpoint of segment XE. Let J be the reflection of point B across point R. Point Z is obtained by rotating point R by angle 7pi/12 about point E. Line V is the angle bisector of angle XZB. Let L be ... | 9.84 | MATH |
[
{
"content": "WE = 12. Let G be the reflection of point W across point E. Let B be the vector from point E to point G. Point S is the translation of point G by vector B. Point C is obtained by rotating point S by angle 5pi/12 about point W. Let J be the perpendicular bisector of segment GW. Let I be the reflect... | 104.03 | MATH |
[
{
"content": "Let NO = 10. Let Y be the rotation of point N by angle pi/4 around point O. Let H be the reflection of point Y across point N. Let E be the perpendicular bisector of segment OY. Point F is the reflection of point N across line E. Point J is the midpoint of segment FH. Let B be the midpoint of segm... | 9.79 | MATH |
[
{
"content": "UP = 8. Point M is the reflection of point U across point P. Line H passes through point M perpendicular to segment UM. Point T is the reflection of point P across line H. Let W be the midpoint of segment UP. Find the distance between points W and T. Express your answer as a decimal number rounded... | 20.0 | MATH |
[
{
"content": "Let LZ = 2. Point O is obtained by rotating point Z by angle pi about point L. Point U is obtained by rotating point L by angle pi/2 about point Z. Point K is the midpoint of segment UZ. Line G is the perpendicular bisector of segment OU. Point X lies on segment ZL. Let F be the perpendicular bise... | 3.2 | MATH |
[
{
"content": "XT = 2. Let A be the vector from point T to point X. Let P be the midpoint of segment XT. Point S is the translation of point X by vector A. Point W is obtained by rotating point P by angle pi/3 about point S. Let G be the line through points T and X. Let H be the line through point S perpendicula... | 3.27 | MATH |
[
{
"content": "Let KV = 11. Point N is obtained by rotating point K by angle 5pi/6 about point V. Let G be the perpendicular bisector of segment VN. Line H passes through point N parallel to line G. Let P be the line through point K perpendicular to line H. Let J be the line through point V perpendicular to line... | 22.0 | MATH |
[
{
"content": "SD = 2. Let E be the midpoint of segment SD. Let R be the perpendicular bisector of segment SD. Let K be the midpoint of segment SE. Point T is the reflection of point D across point S. Let U be the midpoint of segment KE. Point F is the midpoint of segment TE. Point H is the reflection of point U... | 1.8 | MATH |
[
{
"content": "SD = 4. Point A is obtained by rotating point D by angle 7pi/12 about point S. Point Q is the midpoint of segment AD. Point X is the reflection of point S across point Q. Line Y is the angle bisector of angle XQD. Point M is the reflection of point D across line Y. What is the length of segment MQ... | 3.17 | MATH |
[
{
"content": "Let WU = 7. Let G be the perpendicular bisector of segment UW. Point R lies on line G at distance 3 from point U. Point H is the reflection of point R across point U. Point Q is the midpoint of segment UW. Let X be the perpendicular bisector of segment QR. Line P is the reflection of line X across... | 12.41 | MATH |
[
{
"content": "FB = 7. Let E be the rotation of point F by angle 5pi/6 around point B. Let P be the rotation of point B by angle 3pi/4 around point E. Let U be the rotation of point F by angle pi/6 around point E. Let A be the reflection of point F across point P. Point N is the midpoint of segment FU. Let L be ... | 38.24 | MATH |
[
{
"content": "Let EB = 10. Let Z be the rotation of point B by angle pi/6 around point E. Let O be the reflection of point B across point E. Let H be the reflection of point O across point Z. Point C is the reflection of point E across point H. Let A be the vector from point O to point Z. Let U be the perpendic... | 53.98 | MATH |
[
{
"content": "Let XQ = 6. Point P is obtained by rotating point X by angle 7pi/12 about point Q. Let Z be the perpendicular bisector of segment QX. Line H passes through point P perpendicular to line Z. Point N is the reflection of point P across line Z. Point A is the midpoint of segment QN. Point S is the ref... | 9.2 | MATH |
[
{
"content": "Let ZC = 5. Let J be the midpoint of segment ZC. Line F is the perpendicular bisector of segment ZC. Let N be the rotation of point Z by angle pi/12 around point C. Point M is the reflection of point J across point N. Let D be the line through point C parallel to line F. Let G be the angle bisecto... | 5.32 | MATH |
[
{
"content": "Let GI = 10. Line N passes through points I and G. Let A be the perpendicular bisector of segment IG. Let X be the vector from point G to point I. Point Z is obtained by rotating point I by angle pi/4 about point G. Let P be the reflection of line A through point I. Let Y be point Z translated by ... | 87.54 | MATH |
[
{
"content": "Let KP = 12. Let X be the vector from point P to point K. Let I be the rotation of point K by angle 3pi/4 around point P. Line W passes through points K and I. Line M passes through points K and P. Point J is the reflection of point I across point K. Point D is the translation of point K by vector... | 23.74 | MATH |
[
{
"content": "Let BF = 11. Line A is the perpendicular bisector of segment BF. Let J be the line through point F parallel to line A. Let O be the reflection of point F across point B. Let V be the rotation of point B by angle 5pi/6 around point O. Let U be the reflection of point B across point O. Point R is ob... | 21.54 | MATH |
[
{
"content": "Let MT = 10. Point L is the reflection of point T across point M. Let N be the perpendicular bisector of segment ML. Let X be the perpendicular bisector of segment MT. Point W is the midpoint of segment MT. Point O is the reflection of point T across line N. Point U is on line X with |UO| = 3. Let... | 12.59 | MATH |
[
{
"content": "BV = 7. Point Z is the midpoint of segment BV. Let N be the rotation of point B by angle 2pi/3 around point Z. Let E be the vector from point B to point V. Line J passes through points V and N. Let I be point V translated by vector E. Line Y passes through point V perpendicular to line J. Point O ... | 3.5 | MATH |
[
{
"content": "Let AX = 4. Let Q be the rotation of point A by angle pi/6 around point X. Point F is the reflection of point X across point A. Point G is the reflection of point Q across point X. Let H be the reflection of point G across point F. Point D is the midpoint of segment XQ. Point W is the midpoint of ... | 24.09 | MATH |
[
{
"content": "Let VM = 7. Let S be the midpoint of segment VM. Line J passes through points S and M. Let R be the line through point V perpendicular to line J. Point N is the reflection of point M across line R. Find the distance between points N and V. Express your answer as a decimal number rounded to 2 decim... | 7.0 | MATH |
[
{
"content": "TZ = 10. Let Y be the rotation of point T by angle 11pi/12 around point Z. Let F be the midpoint of segment TZ. Line B is the perpendicular bisector of segment TF. Point H is on line B with |HZ| = 10. Point S is the reflection of point Y across line B. Point W is the midpoint of segment YS. Point ... | 26.35 | MATH |
[
{
"content": "TH = 7. Let W be the perpendicular bisector of segment HT. Line Q is the reflection of line W across point T. Let U be the reflection of point H across point T. Line A is the reflection of line Q across line W. Point S lies on line A at distance 10 from point T. Point Y is the midpoint of segment ... | 9.67 | MATH |
[
{
"content": "DK = 4. P is constructed so that KP = 2. Point J is obtained by rotating point P by angle 5pi/12 about point K. Point E is the reflection of point P across point K. Point F is the reflection of point J across point P. Point Q is the reflection of point F across segment EK. Find the distance betwee... | 5.81 | MATH |
[
{
"content": "Let RK = 9. Let M be the rotation of point K by angle pi/2 around point R. Let O be the rotation of point R by angle pi/4 around point M. Point J is the midpoint of segment KR. Let D be the midpoint of segment KO. Point C is the reflection of point J across point D. What is the length of segment C... | 6.89 | MATH |
[
{
"content": "WA = 3. Let B be the reflection of point A across point W. Let R be the reflection of point A across point B. Let U be the line through point B perpendicular to segment AW. Let D be the reflection of line U through point R. Point P is on line U. Point O is the reflection of point P across line D. ... | 24.0 | MATH |
[
{
"content": "MN = 8. Let H be the line through points M and N. Line J passes through point M perpendicular to line H. Let U be the rotation of point M by angle pi/12 around point N. Point G is obtained by rotating point U by angle pi/4 about point M. Let V be the vector from point U to point N. Let R be the li... | 57.45 | MATH |
[
{
"content": "Let MS = 12. Let C be the perpendicular bisector of segment SM. Line J passes through point M parallel to line C. Point Y is obtained by rotating point S by angle pi about point M. Let G be the reflection of line J through point S. Let I be the midpoint of segment MY. Point W is the reflection of ... | 120.0 | MATH |
[
{
"content": "QV = 1. Let G be the line through points Q and V. Point B is on line G with |BV| = 7. Point E is obtained by rotating point V by angle pi/3 about point Q. Line A is the perpendicular bisector of segment VQ. Line X is the perpendicular bisector of segment EQ. Line T passes through point Q parallel ... | 2.09 | MATH |
[
{
"content": "BE = 4. Point G is the reflection of point B across point E. Let A be the rotation of point E by angle 11pi/12 around point B. Let N be the midpoint of segment BA. Let U be the midpoint of segment GN. Point L is the midpoint of segment AU. What is the length of segment NL? Express your answer as a... | 1.52 | MATH |
[
{
"content": "Let ZU = 1. Point Q is the reflection of point U across point Z. Point S is obtained by rotating point Z by angle pi/12 about point Q. Point L is the reflection of point S across segment UZ. Let I be the midpoint of segment UZ. Let K be the midpoint of segment IL. Let N be the reflection of point ... | 0.71 | MATH |
[
{
"content": "Let WI = 9. Point M is obtained by rotating point I by angle 3pi/4 about point W. Let G be the angle bisector of angle WMI. Line D passes through point I parallel to line G. Point E is obtained by rotating point I by angle 7pi/12 about point W. Line Z is the reflection of line D across line G. Let... | 13.7 | MATH |
[
{
"content": "Let CK = 5. Point O is the reflection of point K across point C. Let Z be the perpendicular bisector of segment OK. Line M passes through point O parallel to line Z. Point R is the reflection of point C across line M. Point V is the reflection of point R across line Z. Point I is the midpoint of s... | 20.0 | MATH |
[
{
"content": "Let AB = 1. Let AD = 4. Point N is obtained by rotating point A by angle 5pi/6 about point D. Line G is the perpendicular bisector of segment DN. Let H be the line through point B parallel to line G. Point P is on line H. Point J is the reflection of point D across point N. Let S be the reflection... | 8.0 | MATH |
[
{
"content": "Let NM = 12. Line O passes through points N and M. Let A be the line through point M perpendicular to line O. Let Z be the rotation of point N by angle 7pi/12 around point M. Let F be the reflection of line A through point Z. Let L be the line through point Z parallel to line F. Point B is the ref... | 44.09 | MATH |
[
{
"content": "Let PR = 10. Let Q be the reflection of point P across point R. Let Z be the rotation of point P by angle 5pi/6 around point Q. Let U be the midpoint of segment ZQ. Let O be the line through points Q and U. Point C is the reflection of point R across point Q. Point X is on line O. Point F is the r... | 0.52 | MATH |
[
{
"content": "Let IZ = 12. Point R is the reflection of point Z across point I. Point M is the reflection of point R across point Z. Point O is the midpoint of segment ZI. Point C is the midpoint of segment MO. Find the distance between points C and R. Express your answer as a decimal number rounded to 2 decima... | 33.0 | MATH |
[
{
"content": "Let NA = 1. Let K be the rotation of point A by angle 11pi/12 around point N. Point V is the midpoint of segment NK. Let U be the midpoint of segment VK. Point P is the reflection of point U across segment KA. What is the length of segment PK? Express your answer as a decimal number rounded to 2 d... | 0.25 | MATH |
[
{
"content": "RL = 7. Line K is the perpendicular bisector of segment RL. Line J passes through point R parallel to line K. Let N be the reflection of point L across point R. Let A be the reflection of line J across line K. Let D be the line through point N parallel to line K. Point G is on line D with |GR| = 1... | 189.65 | MATH |
[
{
"content": "Let IH = 3. Let W be the midpoint of segment HI. Let L be the reflection of point W across point H. Point O is obtained by rotating point W by angle 7pi/12 about point I. Let P be the angle bisector of angle OIH. Point Q is the reflection of point H across line P. Point F is the reflection of poin... | 6.55 | MATH |
[
{
"content": "JP = 4. Line Y is the perpendicular bisector of segment PJ. Let E be the midpoint of segment JP. Let H be the midpoint of segment EP. Let M be the midpoint of segment HE. Point B is obtained by rotating point E by angle 2pi/3 about point M. Point G is the reflection of point M across line Y. Point... | 0.9 | MATH |
[
{
"content": "Let JA = 9. Let F be the rotation of point J by angle 2pi/3 around point A. Line Z is the angle bisector of angle FAJ. Let Q be the line through point J parallel to line Z. Let C be the midpoint of segment AF. Point O is the reflection of point C across point J. Let P be the reflection of point O ... | 31.5 | MATH |
[
{
"content": "ZA = 9. Let N be the midpoint of segment AZ. Let E be the reflection of point N across point A. Point B is the midpoint of segment ZN. Point F is obtained by rotating point A by angle pi/6 about point E. Point P is the midpoint of segment BF. Let T be the line through points P and Z. Line S passes... | 5.04 | MATH |
[
{
"content": "Let PD = 10. Point I is the reflection of point D across point P. Let F be the rotation of point P by angle pi/12 around point I. Line N is the angle bisector of angle FDP. Line Z passes through point D perpendicular to line N. Point V is the reflection of point I across line N. Line E passes thro... | 31.49 | MATH |
[
{
"content": "IJ = 4. Let F be the vector from point I to point J. Let Q be point J translated by vector F. Let U be the rotation of point J by angle 3pi/4 around point Q. Let T be the reflection of point Q across point I. Let E be the rotation of point Q by angle pi/6 around point I. Let P be the rotation of p... | 7.05 | MATH |
[
{
"content": "DU = 12. Point H is obtained by rotating point D by angle 5pi/12 about point U. Let A be the midpoint of segment DH. Let I be the midpoint of segment AD. Point E is the midpoint of segment UI. Find the distance between points A and E. Express your answer as a decimal number rounded to 2 decimal pl... | 5.1 | MATH |
[
{
"content": "Let UJ = 8. Let H be the reflection of point J across point U. Let V be the rotation of point U by angle 11pi/12 around point J. Point P is obtained by rotating point U by angle 2pi/3 about point H. Line M passes through point J perpendicular to segment UH. Point E is the reflection of point P acr... | 3.75 | MATH |
[
{
"content": "Let PD = 4. Point L is the reflection of point P across point D. Let Z be the midpoint of segment LD. Let M be the rotation of point P by angle 3pi/4 around point Z. Point T is the reflection of point L across point M. Line X is the perpendicular bisector of segment MD. Point B is the midpoint of ... | 2.75 | MATH |
[
{
"content": "Let IO = 2. Let A be the reflection of point O across point I. Line J passes through points A and O. Let F be the line through point A perpendicular to line J. Point H is on line F with |HI| = 1. Let Q be the angle bisector of angle HIO. Point S is the reflection of point O across point A. Let D b... | 19.46 | MATH |
[
{
"content": "FW = 12. Line S is the perpendicular bisector of segment FW. Point Y is the reflection of point W across point F. Let A be the rotation of point W by angle pi/2 around point Y. Let Q be the midpoint of segment YA. Point O is the midpoint of segment AF. Line I passes through points A and F. Line G ... | 62.23 | MATH |
[
{
"content": "Let KX = 11. Line Z passes through points X and K. Point F is obtained by rotating point X by angle 7pi/12 about point K. Let M be the line through points K and F. Line C is the reflection of line M across line Z. Let I be the reflection of point K across point X. Let L be the line through point F... | 10.51 | MATH |
[
{
"content": "Let ND = 9. Point Z is obtained by rotating point D by angle pi/3 about point N. Line A is the perpendicular bisector of segment NZ. Point S is the midpoint of segment DZ. Let J be the rotation of point N by angle 7pi/12 around point D. Point Q is the reflection of point S across line A. Let K be ... | 4.9 | MATH |
[
{
"content": "Let WN = 1. Point V is obtained by rotating point W by angle pi/2 about point N. Let Y be the line through points N and V. Point R is the reflection of point W across line Y. Let X be the reflection of point V across point N. Q is placed 4 units away from R. Point F is the reflection of point Q ac... | 1.41 | MATH |
[
{
"content": "FL = 1. Let G be the reflection of point F across point L. Let S be the reflection of point F across point G. Line P is the angle bisector of angle FLG. Point H is the reflection of point S across line P. Line T is the perpendicular bisector of segment GS. Let B be the rotation of point F by angle... | 2.55 | MATH |
[
{
"content": "MB = 10. Point A is the reflection of point B across point M. Let G be the reflection of point B across point A. Point N is the midpoint of segment MB. Let W be the angle bisector of angle GNB. Line R is the reflection of line W across point G. Point U is the reflection of point M across line R. W... | 135.0 | MATH |
[
{
"content": "Let ZK = 2. Let B be the midpoint of segment ZK. Point V is obtained by rotating point B by angle 11pi/12 about point K. Let J be the line through points K and Z. Let T be the perpendicular bisector of segment VB. Let D be the midpoint of segment BK. Line I is the reflection of line T across line ... | 7.66 | MATH |
[
{
"content": "Let JS = 8. Point X is the midpoint of segment JS. Line O is the perpendicular bisector of segment SJ. Let V be the midpoint of segment JX. Point G is the midpoint of segment SV. Point Y lies on line O at distance 3 from point G. Point B is the midpoint of segment YJ. Let N be the midpoint of segm... | 9.44 | MATH |
[
{
"content": "JR = 7. Line V passes through point R perpendicular to segment JR. Point P is the reflection of point R across point J. Let A be the reflection of line V through point J. Let I be the reflection of line A across line V. Point H is the reflection of point J across line I. Point Z is the midpoint of... | 31.5 | MATH |
[
{
"content": "Let QA = 11. Let V be the vector from point A to point Q. Point D is the translation of point Q by vector V. Line U passes through points A and D. Let W be the reflection of point A across point D. Point K is obtained by rotating point W by angle pi/4 about point A. Line Z is the angle bisector of... | 164.48 | MATH |
[
{
"content": "FN = 7. Point G is the midpoint of segment FN. Point S is obtained by rotating point F by angle 7pi/12 about point G. Let Z be the rotation of point F by angle pi/4 around point S. Let E be the midpoint of segment ZS. Point W is the reflection of point F across point E. Point R is the midpoint of ... | 5.66 | MATH |
[
{
"content": "Let AC = 8. Let D be the rotation of point A by angle 7pi/12 around point C. Let F be the angle bisector of angle ADC. Let Z be the midpoint of segment DA. Let Q be the reflection of point C across point A. Let X be the line through point D parallel to segment AC. Line L is the reflection of line ... | 5.66 | MATH |
[
{
"content": "Let PD = 8. Let Q be the perpendicular bisector of segment DP. Point I lies on line Q at distance 9 from point D. Point J is the reflection of point P across segment DI. Let Z be the midpoint of segment PI. Find the length of segment ZJ. Express your answer as a decimal number rounded to 2 decimal... | 11.45 | MATH |
[
{
"content": "Let WY = 8. Let I be the rotation of point Y by angle 2pi/3 around point W. Line S is the perpendicular bisector of segment WI. Let P be the line through point W parallel to line S. Line P and segment IY intersect at point A. Point X is the reflection of point A across segment YW. Find the distanc... | 4.62 | MATH |
[
{
"content": "Let IO = 5. Let Y be the rotation of point I by angle pi/12 around point O. S is placed 6 units away from O. Let Q be the angle bisector of angle SOI. Point Z is the reflection of point S across line Q. Let A be the rotation of point I by angle pi/3 around point Z. Point U is the reflection of poi... | 1.02 | MATH |
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