messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let BE = 9. Let Y be the line through points E and B. Point N is obtained by rotating point B by angle pi/6 about point E. Let P be the perpendicular bisector of segment EB. Point O is the reflection of point E across point N. Point I is the reflection of point O across line P. Point G is the refl... | 1.05 | MATH |
[
{
"content": "Let HU = 7. Let O be the midpoint of segment UH. Let J be the vector from point O to point U. Line L is the perpendicular bisector of segment HO. Point V is on line L with |VH| = 11. Let Y be the reflection of point H across point U. Point T is the translation of point Y by vector J. Line S passes... | 45.16 | MATH |
[
{
"content": "Let PK = 3. Point F is the midpoint of segment KP. Let G be the rotation of point K by angle pi/4 around point F. Let W be the line through point P perpendicular to segment PK. Let Q be the line through point G parallel to segment PK. Point T is the reflection of point P across point G. Line X is ... | 2.12 | MATH |
[
{
"content": "BU = 9. Let W be the midpoint of segment UB. Point T is the midpoint of segment UW. Let A be the reflection of point T across point W. Find the distance between points A and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 2.25 | MATH |
[
{
"content": "Let HE = 7. Point M is the midpoint of segment HE. Let V be the vector from point E to point H. Let R be the perpendicular bisector of segment HE. Point S lies on line R at distance 9 from point H. Let X be the line through points H and S. Point T is the translation of point M by vector V. Point N... | 8.16 | MATH |
[
{
"content": "CX = 10. Let E be the reflection of point X across point C. Point Z is obtained by rotating point C by angle pi/4 about point X. Point Y is the reflection of point E across segment CZ. Point M is the midpoint of segment YC. Point L is the midpoint of segment CM. Point R is the reflection of point ... | 5.84 | MATH |
[
{
"content": "Let VS = 10. Line C passes through points V and S. Point X is the reflection of point V across point S. Let N be the reflection of point X across point V. Line U passes through point N perpendicular to line C. Point K is the reflection of point S across line U. Find the distance between points N a... | 30.0 | MATH |
[
{
"content": "AY = 7. Point D is obtained by rotating point A by angle 7pi/12 about point Y. Let T be the vector from point Y to point A. Let U be point D translated by vector T. Line F is the angle bisector of angle AYD. Point Q is obtained by rotating point A by angle pi/2 about point D. Line O is the angle b... | 6.19 | MATH |
[
{
"content": "TN = 6. Let A be the rotation of point T by angle pi/6 around point N. Let F be the reflection of point A across point N. Let Q be the reflection of point A across point F. Let R be the reflection of point N across point Q. Let S be the angle bisector of angle TRQ. Point J is the reflection of poi... | 6.63 | MATH |
[
{
"content": "Let QZ = 9. Let R be the rotation of point Q by angle pi/4 around point Z. Let O be the rotation of point Q by angle 3pi/4 around point Z. Let S be the reflection of point R across point Q. Let D be the midpoint of segment SZ. Point J is the reflection of point D across segment OQ. Line W is the p... | 9.64 | MATH |
[
{
"content": "EU = 10. Let X be the midpoint of segment EU. Line G passes through points E and X. Line V passes through point E perpendicular to line G. Let Y be the midpoint of segment XE. Point J is on line V with |JU| = 3. Point L is the reflection of point X across point U. Point K is the reflection of poin... | 10.11 | MATH |
[
{
"content": "Let YL = 12. Let M be the vector from point Y to point L. Let E be point L translated by vector M. Point X is obtained by rotating point L by angle 11pi/12 about point Y. Let I be the reflection of point E across point Y. Let N be the angle bisector of angle IXY. Let T be the line through point Y ... | 36.0 | MATH |
[
{
"content": "Let GO = 7. Let S be the rotation of point O by angle 7pi/12 around point G. Let W be the perpendicular bisector of segment GO. Line T is the reflection of line W across point S. Line I is the reflection of line T across line W. Point D is the reflection of point S across line I. Point B is the mi... | 18.9 | MATH |
[
{
"content": "US = 9. Let R be the midpoint of segment SU. Point O is the midpoint of segment RS. Let Q be the rotation of point S by angle pi/2 around point R. Point K is the reflection of point O across segment QS. Let C be the line through points R and K. Point P is the intersection of segment QS and line C.... | 2.4 | MATH |
[
{
"content": "NZ = 1. Point S is obtained by rotating point Z by angle 7pi/12 about point N. Point K is the reflection of point N across segment ZS. Point L is the midpoint of segment SN. Point F is the reflection of point L across point S. Find the distance between points F and K. Express your answer as a deci... | 1.23 | MATH |
[
{
"content": "IT = 7. Let G be the rotation of point I by angle 7pi/12 around point T. Let P be the reflection of point T across point G. Point U is the reflection of point P across point I. Line K is the perpendicular bisector of segment IP. Let R be the line through point U parallel to line K. Point Z is the ... | 78.51 | MATH |
[
{
"content": "Let UT = 4. Point L is obtained by rotating point T by angle 5pi/12 about point U. Line J passes through points U and L. Point H is the reflection of point T across line J. Let O be the reflection of point U across point L. Point E is the reflection of point U across point O. What is the distance ... | 15.46 | MATH |
[
{
"content": "SW = 4. Line T is the perpendicular bisector of segment SW. Point F is the reflection of point S across point W. Point U lies on line T at distance 7 from point F. Point M is obtained by rotating point F by angle pi/3 about point W. Let L be the line through point M perpendicular to line T. Point ... | 6.1 | MATH |
[
{
"content": "KD = 2. Let U be the perpendicular bisector of segment KD. Point F is the reflection of point D across point K. Point T is obtained by rotating point F by angle 11pi/12 about point D. Let E be the line through point D parallel to line U. Let Z be the rotation of point K by angle pi/12 around point... | 4.09 | MATH |
[
{
"content": "Let OB = 8. Point G is the midpoint of segment OB. M is constructed so that BM = 5. Let P be the midpoint of segment BM. Point Z is the midpoint of segment BP. Let X be the midpoint of segment PO. Point L is the reflection of point X across segment ZG. What is the length of segment ZL? Express you... | 4.0 | MATH |
[
{
"content": "Let GJ = 3. Let N be the rotation of point G by angle 3pi/4 around point J. Let C be the reflection of point G across point J. Point O is obtained by rotating point G by angle 5pi/12 about point J. Let Q be the midpoint of segment CN. Point R is the reflection of point Q across segment JO. Find th... | 3.81 | MATH |
[
{
"content": "Let RS = 12. Let F be the midpoint of segment SR. Point A is the midpoint of segment SF. Line Y is the perpendicular bisector of segment SA. Let O be the line through point A perpendicular to segment SF. Line X is the reflection of line Y across line O. Line X and segment SF intersect at point N. ... | 7.5 | MATH |
[
{
"content": "HB = 11. Point Q is the reflection of point B across point H. Let L be the midpoint of segment BH. Point T is obtained by rotating point H by angle 2pi/3 about point Q. Let E be the line through points T and Q. Line V is the perpendicular bisector of segment BH. Line I is the reflection of line E ... | 57.42 | MATH |
[
{
"content": "FU = 5. Point W is the reflection of point F across point U. Point H is obtained by rotating point W by angle pi/4 about point U. Let J be the midpoint of segment WH. Point Q is the reflection of point H across segment UF. Line Y is the perpendicular bisector of segment UF. Let O be the reflection... | 14.42 | MATH |
[
{
"content": "Let JY = 9. Let V be the perpendicular bisector of segment YJ. Let D be the midpoint of segment YJ. Let Z be the reflection of point Y across point J. Point U is on line V with |UJ| = 12. Line P is the perpendicular bisector of segment YZ. Let H be the line through point Z parallel to line P. Poin... | 44.32 | MATH |
[
{
"content": "IP = 6. Let Q be the midpoint of segment IP. Let D be the reflection of point I across point P. Point M is the reflection of point Q across point D. Let X be the midpoint of segment QI. Find the length of segment MX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent t... | 19.5 | MATH |
[
{
"content": "Let PM = 6. Let U be the rotation of point P by angle pi/2 around point M. Let T be the angle bisector of angle UMP. Let Q be the midpoint of segment UP. Let B be the midpoint of segment MU. Let I be the line through point B perpendicular to line T. Point L is the reflection of point U across line... | 6.0 | MATH |
[
{
"content": "JO = 2. Let K be the rotation of point O by angle pi/4 around point J. Let V be the line through points J and O. Point Q is the midpoint of segment OJ. Line M is the angle bisector of angle JKQ. Let Z be the reflection of line V across line M. Point A is the reflection of point K across line Z. Po... | 1.86 | MATH |
[
{
"content": "MS = 8. Let K be the rotation of point S by angle 5pi/6 around point M. Let N be the rotation of point K by angle pi/3 around point M. Let W be the midpoint of segment SN. Point B is obtained by rotating point W by angle pi about point K. Point U is the reflection of point M across point N. Line X... | 10.9 | MATH |
[
{
"content": "WD = 12. Let N be the reflection of point W across point D. Let V be the midpoint of segment DN. Point F is obtained by rotating point N by angle 7pi/12 about point W. Line Z passes through points F and W. Point R is the reflection of point D across line Z. Point J is the midpoint of segment VD. L... | 49.67 | MATH |
[
{
"content": "SL = 5. Point N is obtained by rotating point L by angle 7pi/12 about point S. Let T be the rotation of point S by angle pi/4 around point N. Point H is the midpoint of segment NL. Let C be the reflection of point H across point N. Let U be the line through point C parallel to segment NT. Point M ... | 3.97 | MATH |
[
{
"content": "AY = 1. Let N be the perpendicular bisector of segment YA. Let H be the reflection of line N through point Y. Let U be the rotation of point A by angle 7pi/12 around point Y. Point Q is the reflection of point Y across line H. Let L be the midpoint of segment YQ. Point M is the midpoint of segment... | 0.95 | MATH |
[
{
"content": "BN = 4. Let J be the line through points B and N. Point Y is obtained by rotating point B by angle 7pi/12 about point N. Point A is the midpoint of segment NB. Let X be the rotation of point A by angle 11pi/12 around point Y. Point K is the midpoint of segment AX. Point D is the reflection of poin... | 4.32 | MATH |
[
{
"content": "Let TC = 5. Let H be the midpoint of segment TC. Let TN = 1. Line I is the angle bisector of angle HTN. Let O be the reflection of line I through point H. Point W is on segment NT. Line X passes through point W perpendicular to segment NT. Line J is the reflection of line X across line I. Line S i... | 0.25 | MATH |
[
{
"content": "Let HR = 1. Let Q be the reflection of point H across point R. Let W be the rotation of point Q by angle pi/12 around point R. Let Z be the rotation of point W by angle pi around point Q. Line T is the perpendicular bisector of segment ZQ. Line K passes through point H parallel to line T. Let X be... | 0.52 | MATH |
[
{
"content": "KM = 4. Let Y be the midpoint of segment KM. Line Z is the perpendicular bisector of segment YM. Point E is the reflection of point K across line Z. Let F be the rotation of point K by angle 3pi/4 around point E. Line H is the angle bisector of angle FMK. Point Q is the reflection of point Y acros... | 11.26 | MATH |
[
{
"content": "Let HR = 11. Let S be the reflection of point H across point R. Let V be the rotation of point H by angle 3pi/4 around point R. Let J be the rotation of point R by angle pi/2 around point V. Let U be the reflection of point S across point J. Point W is obtained by rotating point S by angle 2pi/3 a... | 46.35 | MATH |
[
{
"content": "DA = 3. Let O be the midpoint of segment DA. Point M is the midpoint of segment AO. Let L be the midpoint of segment MO. Let Q be the midpoint of segment LD. Let W be the reflection of point D across point L. Let G be the midpoint of segment DQ. Line T is the perpendicular bisector of segment LD. ... | 2.86 | MATH |
[
{
"content": "Let RQ = 5. Point G is obtained by rotating point Q by angle pi/2 about point R. Point W is the reflection of point G across point R. Let O be the rotation of point G by angle 7pi/12 around point Q. Point J is the reflection of point W across point O. Point Z is the midpoint of segment OJ. Line S ... | 2.6 | MATH |
[
{
"content": "ME = 10. Let T be the rotation of point E by angle pi/12 around point M. Point Y is the midpoint of segment ET. Line J is the perpendicular bisector of segment YT. Line Q is the reflection of line J across point Y. Point S is the reflection of point M across line Q. What is the distance between po... | 1.31 | MATH |
[
{
"content": "QK = 11. Point Y is the midpoint of segment KQ. Point A is the reflection of point Q across point K. Let W be the rotation of point K by angle pi/4 around point Y. Point V is the midpoint of segment YA. Point P is the midpoint of segment WA. Point N is the reflection of point Y across point Q. Poi... | 40.49 | MATH |
[
{
"content": "YB = 2. Let H be the midpoint of segment BY. Let W be the perpendicular bisector of segment YB. Line Q is the reflection of line W across point B. Let S be the reflection of point H across point B. Let U be the line through point B perpendicular to line Q. Point F is obtained by rotating point S b... | 2.88 | MATH |
[
{
"content": "VO = 6. Let X be the vector from point O to point V. Point B is the translation of point V by vector X. Point Q is obtained by rotating point V by angle 3pi/4 about point O. Let R be the rotation of point O by angle pi/3 around point Q. Let M be the angle bisector of angle QRO. Line S passes throu... | 13.16 | MATH |
[
{
"content": "JW = 1. Point F is obtained by rotating point J by angle pi/3 about point W. Line Y passes through points W and F. Point I is the reflection of point J across line Y. Point B is the reflection of point J across point F. Let Z be the midpoint of segment BI. What is the length of segment ZB? Express... | 0.5 | MATH |
[
{
"content": "UM = 4. Let D be the rotation of point M by angle pi/3 around point U. Line S passes through points M and D. Let L be the midpoint of segment UD. Let C be the midpoint of segment LM. Let E be the midpoint of segment LD. Point V is the reflection of point C across line S. Point J is the midpoint of... | 1.87 | MATH |
[
{
"content": "Let XN = 4. Let R be the vector from point N to point X. Let O be the rotation of point X by angle 7pi/12 around point N. Point E is the translation of point X by vector R. Let S be the reflection of point X across point E. Point J is obtained by rotating point O by angle pi/3 about point E. Let B... | 6.06 | MATH |
[
{
"content": "PI = 1. Point V is obtained by rotating point I by angle pi/12 about point P. Let A be the midpoint of segment PV. Let F be the angle bisector of angle IAP. Point T is the reflection of point V across point P. Point C is the midpoint of segment PI. Let X be the line through point P parallel to lin... | 1.58 | MATH |
[
{
"content": "QJ = 5. Point M is obtained by rotating point J by angle 11pi/12 about point Q. Let H be the reflection of point M across point Q. Point N is the midpoint of segment QH. Point P is the reflection of point N across segment JQ. Find the length of segment PH. Express your answer as a decimal number r... | 3.1 | MATH |
[
{
"content": "Let UC = 11. Let T be the rotation of point U by angle 11pi/12 around point C. Let G be the rotation of point U by angle pi/3 around point T. Point V is the midpoint of segment TG. Point F is the midpoint of segment UV. Let L be the midpoint of segment FU. Line Q is the angle bisector of angle VGC... | 38.72 | MATH |
[
{
"content": "ID = 3. Let G be the reflection of point I across point D. Line P is the angle bisector of angle GDI. Line Z passes through point D perpendicular to line P. Point Y lies on line P at distance 5 from point D. Let B be the rotation of point D by angle pi/12 around point Y. Line K is the reflection o... | 6.01 | MATH |
[
{
"content": "Let AW = 10. Let D be the line through points A and W. Point F is the reflection of point W across point A. Let K be the vector from point W to point A. Line N passes through point W perpendicular to line D. Let M be the midpoint of segment FA. Point P is the translation of point M by vector K. Po... | 32.91 | MATH |
[
{
"content": "Let YX = 4. Let YL = 2. Let V be the perpendicular bisector of segment LY. Point Z is the reflection of point L across point X. Point E is on line V with |EZ| = 2. Point M is obtained by rotating point E by angle pi/2 about point X. Let G be the midpoint of segment MX. Point N is the reflection of... | 4.0 | MATH |
[
{
"content": "Let KA = 11. Line O passes through points K and A. Point Y is the reflection of point A across point K. Point G is obtained by rotating point A by angle pi/3 about point Y. Line V passes through point G parallel to line O. Point H is the reflection of point K across point A. Point F is the reflect... | 171.83 | MATH |
[
{
"content": "DK = 8. Let S be the reflection of point K across point D. Let Q be the reflection of point D across point K. Let L be the rotation of point Q by angle 11pi/12 around point K. Line B is the perpendicular bisector of segment LD. Line T passes through point L parallel to line B. Let Y be the midpoin... | 4.48 | MATH |
[
{
"content": "DI = 12. Point T is obtained by rotating point I by angle 7pi/12 about point D. Let F be the vector from point D to point T. Let Y be the midpoint of segment ID. Let X be the line through point I parallel to segment YT. Let C be the reflection of line X through point T. Line P passes through point... | 9.72 | MATH |
[
{
"content": "Let GN = 2. Let T be the reflection of point G across point N. Point Y is the reflection of point N across point T. Point U is obtained by rotating point T by angle pi/3 about point G. Let A be the angle bisector of angle UNT. Line E is the perpendicular bisector of segment NU. Line P is the angle... | 24.18 | MATH |
[
{
"content": "CO = 9. Point S is the midpoint of segment CO. Let M be the rotation of point S by angle 2pi/3 around point C. Point H is the midpoint of segment OS. Let T be the vector from point C to point H. Point W is the translation of point H by vector T. Let L be point M translated by vector T. Point V is ... | 10.22 | MATH |
[
{
"content": "EM = 12. Point D is the midpoint of segment ME. Line C is the perpendicular bisector of segment ME. Point J is on line C with |JD| = 6. Point S is the reflection of point J across segment ME. Let G be the midpoint of segment ED. Point A is the midpoint of segment SE. What is the measure of angle E... | 0.79 | MATH |
[
{
"content": "XR = 6. Point F is obtained by rotating point X by angle 5pi/12 about point R. Point U is obtained by rotating point F by angle pi/12 about point R. Point L is the midpoint of segment RU. Point K is the reflection of point L across segment UF. Let T be the midpoint of segment XK. What is the lengt... | 2.28 | MATH |
[
{
"content": "JZ = 9. Let T be the reflection of point J across point Z. Let K be the perpendicular bisector of segment JT. Point A is the midpoint of segment ZJ. Point Y is obtained by rotating point A by angle pi/2 about point T. Let E be the perpendicular bisector of segment JA. Let M be the reflection of li... | 32.22 | MATH |
[
{
"content": "AM = 12. Point P is the reflection of point A across point M. Point I is obtained by rotating point P by angle pi/4 about point M. Let G be the perpendicular bisector of segment PM. Let F be the line through point P perpendicular to line G. Let T be the rotation of point I by angle pi/12 around po... | 26.18 | MATH |
[
{
"content": "RB = 2. Let X be the vector from point R to point B. Let E be the rotation of point B by angle pi/3 around point R. Point T is the reflection of point E across point R. Let Q be the line through points B and T. Point A is the translation of point T by vector X. Let P be the rotation of point T by ... | 1.59 | MATH |
[
{
"content": "Let AS = 8. Let L be the reflection of point A across point S. Let Z be the vector from point A to point L. Point C is the midpoint of segment LS. Point X is obtained by rotating point A by angle 11pi/12 about point L. Let B be the perpendicular bisector of segment LX. Let D be the rotation of poi... | 4.21 | MATH |
[
{
"content": "NF = 9. S is placed 6 units away from F. Let NW = 1. Point B is the midpoint of segment SF. Point M is the reflection of point B across segment WS. Point K is the reflection of point F across segment WS. Find the distance between points M and K. Express your answer as a decimal number rounded to 2... | 3.0 | MATH |
[
{
"content": "Let VC = 1. Let Z be the vector from point V to point C. Point R is obtained by rotating point V by angle 5pi/12 about point C. Let Y be the vector from point R to point C. Point G is obtained by rotating point C by angle pi/12 about point R. Point D is the translation of point G by vector Y. Poin... | 2.4 | MATH |
[
{
"content": "FS = 9. Point L is obtained by rotating point F by angle 5pi/6 about point S. Point T is the reflection of point F across point L. Let K be the reflection of point L across point S. Let O be the reflection of point K across point T. Point I is the midpoint of segment SL. Let G be the midpoint of s... | 3.02 | MATH |
[
{
"content": "EW = 3. Let Q be the perpendicular bisector of segment EW. Let B be the rotation of point E by angle pi/4 around point W. Point G is the midpoint of segment BW. Point D is the midpoint of segment EB. Let H be the line through point E perpendicular to line Q. Let A be the midpoint of segment ED. Le... | 9.95 | MATH |
[
{
"content": "FM = 9. Point D is obtained by rotating point F by angle 2pi/3 about point M. Point E is obtained by rotating point F by angle pi/4 about point M. Let K be the rotation of point D by angle 5pi/6 around point F. Let I be the vector from point D to point F. Let O be point M translated by vector I. L... | 8.36 | MATH |
[
{
"content": "Let JF = 6. Point Q is the reflection of point F across point J. Let P be the angle bisector of angle FQJ. Let W be the line through point F perpendicular to line P. JC = 9. Line L is the perpendicular bisector of segment QJ. Point Y lies on line L at distance 12 from point Q. Point N is the refle... | 15.0 | MATH |
[
{
"content": "WR = 2. Point H is the reflection of point R across point W. Let X be the midpoint of segment RW. Let F be the perpendicular bisector of segment HX. Point K is the reflection of point X across point H. Point D is the reflection of point H across point K. Point T is the reflection of point K across... | 41.87 | MATH |
[
{
"content": "Let SC = 6. Let I be the rotation of point S by angle pi/6 around point C. Let O be the line through point C perpendicular to segment CS. Point F is the reflection of point I across line O. Point B is the midpoint of segment CS. Point N is the midpoint of segment BI. Let G be the midpoint of segme... | 0.93 | MATH |
[
{
"content": "Let OM = 9. Point E is the reflection of point M across point O. Line B passes through points O and E. Point I is the reflection of point O across point M. Let D be the rotation of point I by angle 5pi/12 around point O. Let Q be the midpoint of segment MD. Let J be the midpoint of segment IQ. Poi... | 19.58 | MATH |
[
{
"content": "RV = 1. Point F is the midpoint of segment VR. Point K is the reflection of point F across point V. Let H be the rotation of point K by angle 5pi/6 around point V. Point W is the reflection of point R across segment KH. Point Y is the reflection of point R across segment HW. Point Q is the reflect... | 0.47 | MATH |
[
{
"content": "Let MB = 7. Line T passes through points M and B. Point P is the midpoint of segment BM. Let Z be the reflection of point P across point M. Line X passes through point Z perpendicular to line T. Let N be the rotation of point Z by angle 2pi/3 around point B. Point Q is the reflection of point M ac... | 75.6 | MATH |
[
{
"content": "UE = 11. Point A is obtained by rotating point E by angle 7pi/12 about point U. Point L is obtained by rotating point E by angle 2pi/3 about point U. Point H is the midpoint of segment LA. Let T be the midpoint of segment HE. Let D be the midpoint of segment HA. Find the distance between points D ... | 8.73 | MATH |
[
{
"content": "Let JL = 3. JN = 5. Line K is the perpendicular bisector of segment LN. Point O is the reflection of point J across line K. Let V be the midpoint of segment JN. Point T is the reflection of point V across line K. Point W is the reflection of point O across point L. What is the length of segment TW... | 7.5 | MATH |
[
{
"content": "RY = 5. Let K be the midpoint of segment YR. Let F be the angle bisector of angle YKR. Point O is the midpoint of segment RK. Let S be the line through point R parallel to line F. Let I be the reflection of line F across line S. Point Q is the reflection of point R across line I. Find the distance... | 6.25 | MATH |
[
{
"content": "PD = 12. Let Q be the perpendicular bisector of segment DP. Point L is obtained by rotating point P by angle 5pi/12 about point D. Line O is the angle bisector of angle PLD. Point B is the reflection of point L across line Q. Let N be the midpoint of segment LD. Point K is the reflection of point ... | 5.22 | MATH |
[
{
"content": "Let TF = 12. Let W be the reflection of point F across point T. Let S be the line through points T and F. Line X passes through point W perpendicular to line S. Point I is on line X with |IT| = 8. Let C be the reflection of point W across point F. Let A be the midpoint of segment IT. Point L is th... | 19.91 | MATH |
[
{
"content": "GJ = 2. Line V passes through points J and G. Let X be the reflection of point G across point J. Line N is the perpendicular bisector of segment JG. Point E lies on line V. Point Q is the reflection of point E across point G. Point F is on line N with |FX| = 11. Let A be the angle bisector of angl... | 14.05 | MATH |
[
{
"content": "Let IF = 7. Let J be the rotation of point F by angle 11pi/12 around point I. Line T passes through point F perpendicular to segment IF. Let X be the line through point I parallel to line T. Point U is obtained by rotating point J by angle 7pi/12 about point F. Point G is the reflection of point U... | 10.99 | MATH |
[
{
"content": "Let JS = 9. Let K be the reflection of point J across point S. Let Z be the rotation of point K by angle 3pi/4 around point S. Let Y be the reflection of point K across point Z. Let N be the angle bisector of angle SKY. Let V be the reflection of line N through point S. Point O is the reflection o... | 13.51 | MATH |
[
{
"content": "Let DO = 7. Point J is obtained by rotating point D by angle pi/3 about point O. Point L lies on segment OJ. Line P is the angle bisector of angle DOL. Let X be the reflection of line P through point J. Line T passes through point D parallel to segment OJ. Lines X and T intersect at point A. Let S... | 25.24 | MATH |
[
{
"content": "Let VG = 6. Let F be the rotation of point G by angle pi/2 around point V. Point A is obtained by rotating point G by angle 7pi/12 about point F. Let S be the midpoint of segment FV. Point T is the midpoint of segment AF. Let H be the midpoint of segment TS. Point E is the reflection of point H ac... | 21.88 | MATH |
[
{
"content": "OM = 10. Point Q is the reflection of point M across point O. Let U be the perpendicular bisector of segment MO. Point P is the reflection of point Q across line U. Let Z be the perpendicular bisector of segment PM. Point S is the reflection of point O across line Z. Find the distance between poin... | 10.0 | MATH |
[
{
"content": "UB = 7. Let M be the rotation of point B by angle pi/12 around point U. Point V is the reflection of point M across point U. Point D is the reflection of point B across segment UM. Let R be the midpoint of segment VU. Let T be the reflection of point R across point D. Let F be the perpendicular bi... | 7.85 | MATH |
[
{
"content": "Let UC = 1. Point L is obtained by rotating point C by angle 2pi/3 about point U. Let T be the midpoint of segment UL. Let N be the rotation of point L by angle pi/4 around point T. Let I be the perpendicular bisector of segment TC. Point H lies on line I. Point A is the reflection of point U acro... | 0.92 | MATH |
[
{
"content": "Let FH = 3. Line W is the perpendicular bisector of segment FH. Let U be the midpoint of segment HF. Point X is on line W with |XU| = 2. Let P be the midpoint of segment HU. Let G be the angle bisector of angle FUX. Point I is the reflection of point X across line G. Line O passes through point P ... | 5.7 | MATH |
[
{
"content": "ZW = 2. Let C be the rotation of point W by angle pi/6 around point Z. Point T is the midpoint of segment CZ. Point D is the reflection of point T across segment CW. Let F be the line through point Z parallel to segment CW. Point X is obtained by rotating point Z by angle pi/12 about point T. Let ... | 3.53 | MATH |
[
{
"content": "JP = 12. Let V be the rotation of point P by angle pi/3 around point J. Point D is the midpoint of segment JP. Point K is the midpoint of segment VP. Let A be the rotation of point D by angle 5pi/12 around point V. Point U is the midpoint of segment KJ. Let B be the reflection of point U across po... | 19.1 | MATH |
[
{
"content": "OC = 11. Point P is the reflection of point O across point C. Line J passes through point O perpendicular to segment PO. Point U is the midpoint of segment CO. Let H be the reflection of point P across point O. Let B be the perpendicular bisector of segment PO. Let I be the reflection of point H a... | 51.13 | MATH |
[
{
"content": "Let LK = 2. Line W is the perpendicular bisector of segment LK. Point P is obtained by rotating point K by angle 11pi/12 about point L. Line D is the perpendicular bisector of segment LP. Let Z be the reflection of line W through point K. Let X be the reflection of line Z across line W. Let Y be t... | 44.42 | MATH |
[
{
"content": "SB = 1. Let X be the midpoint of segment SB. Point D is the midpoint of segment BX. Let I be the midpoint of segment BD. Let O be the rotation of point S by angle pi/6 around point X. Line G passes through points X and D. Line T passes through points B and O. Let Q be the reflection of line G acro... | 0.88 | MATH |
[
{
"content": "Let NM = 12. Point F is obtained by rotating point M by angle pi/2 about point N. Let W be the vector from point N to point M. Let J be the perpendicular bisector of segment NM. Let X be the line through point N perpendicular to line J. Point P is the reflection of point F across line X. Let D be ... | 10.82 | MATH |
[
{
"content": "Let IG = 6. Let U be the midpoint of segment GI. Let B be the rotation of point G by angle pi/3 around point I. Let M be the vector from point G to point B. Let D be the line through points I and U. Point O is the midpoint of segment GB. Let H be point O translated by vector M. Point K is the refl... | 17.17 | MATH |
[
{
"content": "Let BX = 6. Let I be the reflection of point B across point X. Let J be the rotation of point I by angle 2pi/3 around point B. Point D is the reflection of point J across segment BX. Let C be the line through points D and I. Point Q is the reflection of point B across line C. Let Z be the midpoint... | 9.0 | MATH |
[
{
"content": "Let VH = 5. Let X be the rotation of point H by angle 5pi/12 around point V. Let L be the reflection of point H across point V. Let R be the line through points X and V. Point Y is the reflection of point X across segment HV. Let D be the perpendicular bisector of segment LX. Let A be the reflecti... | 7.36 | MATH |
[
{
"content": "Let ZD = 3. Let S be the rotation of point D by angle 11pi/12 around point Z. Let F be the angle bisector of angle ZDS. Point M is the reflection of point D across point S. Point E is the reflection of point M across point D. Point H is the reflection of point S across line F. Point K is the refle... | 17.81 | MATH |
[
{
"content": "Let EF = 6. Let W be the perpendicular bisector of segment FE. Let I be the midpoint of segment FE. Let G be the rotation of point F by angle 7pi/12 around point I. Point N is the midpoint of segment GE. Point Z is the reflection of point N across point G. Let H be the line through point I paralle... | 5.81 | MATH |
[
{
"content": "ZR = 3. Let I be the rotation of point R by angle pi/4 around point Z. Point K is the reflection of point R across point I. Point G is obtained by rotating point R by angle 5pi/12 about point I. Point A is the midpoint of segment IG. Let D be the rotation of point A by angle pi/4 around point I. P... | 1.36 | MATH |
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