messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let CD = 5. Point W is the midpoint of segment DC. Point K is obtained by rotating point C by angle pi/4 about point D. Point X is obtained by rotating point D by angle pi/2 about point W. Let H be the midpoint of segment XC. Let M be the midpoint of segment KW. Point T is the midpoint of segment ... | 6.71 | MATH |
[
{
"content": "MY = 10. Point G is obtained by rotating point Y by angle 11pi/12 about point M. Line T is the perpendicular bisector of segment MG. Let F be the line through point Y parallel to line T. Point Q is the reflection of point G across line F. Line D passes through point Q parallel to line F. Line J is... | 78.48 | MATH |
[
{
"content": "VJ = 9. Point A is the midpoint of segment VJ. Let C be the reflection of point J across point V. Let R be the rotation of point C by angle pi/2 around point A. Line Y is the angle bisector of angle RCJ. Point D is the reflection of point C across point R. Line L is the perpendicular bisector of s... | 27.33 | MATH |
[
{
"content": "RD = 5. Let U be the vector from point R to point D. Point Y is obtained by rotating point D by angle 7pi/12 about point R. Let O be the midpoint of segment RY. Let X be point O translated by vector U. Point A is the translation of point Y by vector U. Point J is the midpoint of segment DX. Let H ... | 7.21 | MATH |
[
{
"content": "CP = 6. Point A is obtained by rotating point P by angle pi/2 about point C. Let D be the rotation of point A by angle pi/4 around point P. Let Z be the perpendicular bisector of segment CP. Let H be the reflection of point A across point D. Line W is the reflection of line Z across point P. Point... | 43.03 | MATH |
[
{
"content": "TB = 7. Line C passes through points B and T. Point R is the midpoint of segment TB. Let W be the line through point T perpendicular to line C. Point J is on line W with |JT| = 6. Point S is the reflection of point J across line C. Point X is obtained by rotating point R by angle pi/6 about point ... | 6.71 | MATH |
[
{
"content": "Let RY = 8. Point A is obtained by rotating point R by angle pi/3 about point Y. Let D be the rotation of point A by angle 7pi/12 around point R. Point X is obtained by rotating point A by angle pi/6 about point R. Line Q passes through points Y and D. Point P is the reflection of point A across l... | 9.01 | MATH |
[
{
"content": "Let VZ = 10. Let T be the rotation of point V by angle pi/6 around point Z. Let E be the rotation of point T by angle 7pi/12 around point Z. Let Q be the angle bisector of angle ETZ. Point X is the midpoint of segment EZ. Let K be the midpoint of segment TE. Point O is the reflection of point X ac... | 5.88 | MATH |
[
{
"content": "YJ = 2. Point U is the midpoint of segment JY. Point M is the reflection of point Y across point J. Point Q is obtained by rotating point M by angle pi/6 about point Y. Point W is obtained by rotating point Q by angle pi/3 about point M. Let C be the rotation of point J by angle pi/4 around point ... | 0.17 | MATH |
[
{
"content": "Let RW = 12. Point K is obtained by rotating point R by angle pi/3 about point W. Let O be the reflection of point R across point W. Point V is the reflection of point O across point R. Let H be the midpoint of segment KW. Point L is the reflection of point H across point V. Find the distance betw... | 66.81 | MATH |
[
{
"content": "Let AN = 1. Let P be the rotation of point A by angle pi/12 around point N. Let H be the reflection of point P across point N. Let Y be the midpoint of segment NH. Point D is obtained by rotating point N by angle pi/12 about point H. Let I be the midpoint of segment NY. Line Q is the perpendicular... | 1.4 | MATH |
[
{
"content": "XB = 1. Point Q is obtained by rotating point B by angle 3pi/4 about point X. Let K be the vector from point X to point B. Let W be point Q translated by vector K. Let R be the rotation of point X by angle pi around point B. Point J is the midpoint of segment XB. Point H is the reflection of point... | 3.06 | MATH |
[
{
"content": "Let GK = 3. Point R is obtained by rotating point K by angle pi/4 about point G. Let P be the midpoint of segment GR. Let I be the reflection of point G across point R. Line W passes through points I and R. Point O is the reflection of point P across point G. Let T be the line through points K and... | 3.63 | MATH |
[
{
"content": "YP = 7. Point H is on segment YP. Let X be the perpendicular bisector of segment HY. Point Z is the reflection of point P across line X. Point T is the reflection of point Z across point H. Point U is the midpoint of segment ZH. Point K is the reflection of point U across point H. What is the dist... | 3.5 | MATH |
[
{
"content": "Let ZS = 12. Let P be the reflection of point Z across point S. Let G be the reflection of point P across point Z. Let T be the reflection of point G across point P. Let A be the midpoint of segment ZS. Let W be the reflection of point S across point T. Find the distance between points W and A. Ex... | 126.0 | MATH |
[
{
"content": "GC = 12. Let W be the rotation of point C by angle 5pi/6 around point G. Point Z is obtained by rotating point C by angle pi/2 about point W. Point H is obtained by rotating point C by angle 11pi/12 about point W. Point X is the reflection of point C across point H. Point F is the midpoint of segm... | 45.97 | MATH |
[
{
"content": "Let ND = 11. Let Q be the midpoint of segment ND. Point V is obtained by rotating point N by angle pi/12 about point Q. Let K be the midpoint of segment NQ. Let J be the rotation of point D by angle pi/6 around point V. Let O be the line through points J and Q. Let C be the line through point K pa... | 4.23 | MATH |
[
{
"content": "XL = 8. Point Y is the midpoint of segment XL. Let J be the reflection of point Y across point X. Point B is the midpoint of segment XY. Point Q is the reflection of point B across point L. What is the distance between points Q and J? Express your answer as a decimal number rounded to 2 decimal pl... | 18.0 | MATH |
[
{
"content": "Let MR = 1. Let J be the midpoint of segment RM. Let P be the perpendicular bisector of segment MJ. Line A is the perpendicular bisector of segment RJ. Let T be the reflection of line P across line A. Let Q be the midpoint of segment JR. Line F is the perpendicular bisector of segment MQ. Point H ... | 12.22 | MATH |
[
{
"content": "WF = 8. Point P is the reflection of point W across point F. Let Y be the reflection of point W across point P. Let E be the reflection of point Y across point F. Point V is the midpoint of segment EF. Point J is the midpoint of segment YF. Let I be the reflection of point J across point V. Let K ... | 8.0 | MATH |
[
{
"content": "KF = 2. Let R be the midpoint of segment KF. Let C be the midpoint of segment RK. Point Z is the midpoint of segment RF. Let P be the rotation of point R by angle 11pi/12 around point C. Let E be the midpoint of segment PZ. Let X be the midpoint of segment ZR. Point M is the midpoint of segment XC... | 0.13 | MATH |
[
{
"content": "AE = 8. Point Q is the midpoint of segment AE. Let F be the reflection of point Q across point A. Let X be the vector from point F to point A. Point B is obtained by rotating point E by angle 5pi/12 about point Q. Let N be the perpendicular bisector of segment BQ. Let C be the rotation of point F ... | 6.75 | MATH |
[
{
"content": "Let XE = 8. Let Y be the rotation of point E by angle pi/12 around point X. Line V is the angle bisector of angle YEX. Point S is the reflection of point Y across point E. Point G lies on line V at distance 11 from point E. Let K be the reflection of line V through point S. Let N be the reflection... | 22.17 | MATH |
[
{
"content": "Let GW = 3. Let O be the rotation of point W by angle pi/4 around point G. Let B be the midpoint of segment OG. Let D be the midpoint of segment WG. Line X is the angle bisector of angle OGB. Let A be the midpoint of segment OB. Point R is the reflection of point A across point W. Point V is the m... | 303.91 | MATH |
[
{
"content": "UZ = 4. Point K is the reflection of point Z across point U. F is placed 4 units away from Z. Line N is the perpendicular bisector of segment ZK. Let M be the line through point F perpendicular to line N. Let G be the line through point K perpendicular to line M. Point X is the reflection of point... | 16.0 | MATH |
[
{
"content": "Let RF = 3. Line K passes through point F perpendicular to segment FR. Point Q is the midpoint of segment FR. Line O is the angle bisector of angle RQF. Let I be the reflection of line K across line O. Let S be the midpoint of segment QF. Point X is the reflection of point S across line I. Line T ... | 10.5 | MATH |
[
{
"content": "Let MC = 9. Point E is the midpoint of segment MC. Let V be the angle bisector of angle CEM. Let U be the angle bisector of angle CME. Point W lies on line V at distance 11 from point C. Point D is obtained by rotating point C by angle 5pi/6 about point W. Line Q passes through points D and C. Poi... | 11.88 | MATH |
[
{
"content": "Let BG = 12. Let A be the midpoint of segment BG. Let W be the rotation of point B by angle 11pi/12 around point A. Point P is the reflection of point W across point G. Let V be the reflection of point G across point P. Point L is the reflection of point V across segment AP. Let Z be the midpoint ... | 5.14 | MATH |
[
{
"content": "Let BZ = 12. Let U be the rotation of point B by angle pi/2 around point Z. Point A is the midpoint of segment ZU. Let V be the rotation of point A by angle pi/2 around point Z. Line H passes through points Z and V. Point C is the reflection of point A across line H. Point R is the midpoint of seg... | 13.58 | MATH |
[
{
"content": "SK = 3. Let J be the midpoint of segment SK. Let Z be the line through points S and J. Let W be the rotation of point J by angle 5pi/6 around point K. Point Q is the reflection of point K across segment WJ. Point X is the reflection of point Q across line Z. Point U is the midpoint of segment SQ. ... | 1.8 | MATH |
[
{
"content": "Let ND = 2. Line F is the perpendicular bisector of segment ND. Let T be the line through point D parallel to line F. Point H is the midpoint of segment ND. Let X be the vector from point H to point N. Point S is the midpoint of segment DH. Line E passes through point N parallel to line T. Point O... | 11.42 | MATH |
[
{
"content": "Let ON = 10. Let U be the midpoint of segment ON. Line W is the perpendicular bisector of segment UO. Let B be the rotation of point N by angle 5pi/6 around point U. Let L be the line through point B parallel to line W. Point G is the reflection of point B across segment ON. Let A be the perpendic... | 31.2 | MATH |
[
{
"content": "Let JY = 2. Let X be the reflection of point Y across point J. Point D is the midpoint of segment JX. Point N is the midpoint of segment YD. Point I is the midpoint of segment XN. Point P is obtained by rotating point J by angle pi about point I. Line Q is the angle bisector of angle XPD. Let O be... | 0.3 | MATH |
[
{
"content": "Let SN = 2. Let E be the rotation of point S by angle 5pi/12 around point N. Let V be the rotation of point N by angle 2pi/3 around point E. Let D be the rotation of point S by angle pi/6 around point E. Let C be the reflection of point N across point V. Let R be the reflection of point E across p... | 3.7 | MATH |
[
{
"content": "DG = 2. Let S be the midpoint of segment DG. Let W be the reflection of point S across point D. Let Y be the angle bisector of angle WDG. Let Z be the reflection of line Y through point S. Line U is the reflection of line Z across line Y. Let B be the perpendicular bisector of segment SD. Line F i... | 4.0 | MATH |
[
{
"content": "XB = 5. Let K be the perpendicular bisector of segment XB. Point Z lies on line K at distance 2 from point B. Point L is the reflection of point Z across segment BX. Let G be the midpoint of segment LB. Let Q be the midpoint of segment GZ. Let F be the vector from point X to point Z. Let T be poin... | 3.11 | MATH |
[
{
"content": "SE = 12. Point Y is obtained by rotating point E by angle 7pi/12 about point S. Line H passes through points S and E. Line G passes through point E perpendicular to segment YS. Let K be the midpoint of segment YS. Let X be the line through point K parallel to line H. Point Z is the reflection of p... | 27.52 | MATH |
[
{
"content": "JZ = 4. Let D be the rotation of point Z by angle pi/2 around point J. Point K is the reflection of point J across point D. Let S be the rotation of point K by angle 3pi/4 around point D. Let L be the rotation of point J by angle pi around point Z. Point E is the reflection of point L across segme... | 5.16 | MATH |
[
{
"content": "Let YJ = 1. Line N is the perpendicular bisector of segment YJ. Point K is obtained by rotating point Y by angle pi/12 about point J. Let F be the reflection of point K across point J. Let G be the vector from point F to point Y. Point W is the reflection of point F across line N. Point A is the t... | 2.5 | MATH |
[
{
"content": "HM = 5. Point U is obtained by rotating point H by angle pi/3 about point M. Point J is the reflection of point M across point H. Line Q passes through points J and U. Point L is on line Q. Let K be the midpoint of segment JL. What is the measure of angle KJM, in radians? Express your answer as a ... | 0.52 | MATH |
[
{
"content": "LU = 6. Let J be the midpoint of segment UL. Point Z is the reflection of point J across point L. Let M be the perpendicular bisector of segment UL. Line T is the perpendicular bisector of segment LJ. Point G is the reflection of point L across point Z. Line O passes through point G parallel to li... | 11.33 | MATH |
[
{
"content": "Let HO = 8. Line T is the perpendicular bisector of segment HO. Point P is the midpoint of segment OH. Let R be the rotation of point P by angle pi/6 around point O. Line A is the perpendicular bisector of segment HR. Line L is the reflection of line T across line A. Point Q is the intersection of... | 0.59 | MATH |
[
{
"content": "Let ZX = 5. Let K be the midpoint of segment XZ. Let L be the reflection of point K across point Z. Line D is the angle bisector of angle ZKX. Point M is on line D. Let C be the reflection of line D through point Z. Point J is the reflection of point X across line C. Let P be the line through poin... | 5.0 | MATH |
[
{
"content": "WX = 10. Let S be the midpoint of segment XW. Point L is the midpoint of segment SW. Line C is the perpendicular bisector of segment WL. Let N be the rotation of point W by angle 5pi/6 around point S. Line J passes through point X parallel to line C. Point M is the reflection of point N across lin... | 12.9 | MATH |
[
{
"content": "WT = 2. Let E be the vector from point T to point W. Point D is obtained by rotating point W by angle 2pi/3 about point T. Point C is the translation of point W by vector E. Point B is obtained by rotating point C by angle 5pi/12 about point D. Point S is the reflection of point D across point B. ... | 27.1 | MATH |
[
{
"content": "AB = 10. Let S be the rotation of point B by angle pi/3 around point A. Point H is the midpoint of segment AS. Let P be the midpoint of segment SH. Let D be the midpoint of segment BS. Let T be the line through point D parallel to segment BP. Point U is the reflection of point P across line T. Poi... | 5.5 | MATH |
[
{
"content": "Let WA = 2. Point U is obtained by rotating point A by angle pi/4 about point W. Let P be the angle bisector of angle WAU. Point G is the reflection of point W across point U. Let N be the angle bisector of angle WGA. Point L is the reflection of point U across point G. Line E passes through point... | 3.88 | MATH |
[
{
"content": "Let NP = 4. Point K is obtained by rotating point N by angle 11pi/12 about point P. Point Y is the reflection of point K across point N. Let M be the rotation of point Y by angle pi/4 around point K. Let B be the reflection of point P across point Y. Point S is the midpoint of segment YN. Point O ... | 23.22 | MATH |
[
{
"content": "Let SO = 12. Line W is the perpendicular bisector of segment OS. Point V lies on line W at distance 9 from point O. Line G passes through point S parallel to line W. Point I is the midpoint of segment SO. Point A is the reflection of point O across line G. Point F is the midpoint of segment SA. Po... | 21.63 | MATH |
[
{
"content": "Let ZJ = 7. Let S be the perpendicular bisector of segment ZJ. Point G is obtained by rotating point Z by angle 3pi/4 about point J. Let N be the rotation of point G by angle 11pi/12 around point Z. Point V is on line S with |VJ| = 11. Point R is the midpoint of segment VZ. Point X is the midpoint... | 5.77 | MATH |
[
{
"content": "XZ = 4. Let N be the rotation of point Z by angle pi/12 around point X. Let D be the rotation of point Z by angle 3pi/4 around point N. Point O is the midpoint of segment ZD. Point T is the reflection of point N across segment ZD. Let H be the midpoint of segment DT. Find the length of segment OH.... | 0.52 | MATH |
[
{
"content": "IN = 5. Let C be the reflection of point N across point I. Let F be the rotation of point N by angle 11pi/12 around point C. Line O passes through points F and C. Let A be the midpoint of segment FN. Let Z be the angle bisector of angle CAN. Let R be the reflection of point I across point A. Let Q... | 6.81 | MATH |
[
{
"content": "Let ES = 1. Line G is the perpendicular bisector of segment ES. Point Z is obtained by rotating point E by angle 2pi/3 about point S. Let D be the reflection of point Z across point E. Line O passes through point E parallel to line G. Point P is the reflection of point Z across line O. Point T is ... | 0.52 | MATH |
[
{
"content": "Let KP = 5. Let B be the vector from point P to point K. Let U be the line through points K and P. Let R be the line through point K perpendicular to line U. Point X is obtained by rotating point P by angle 7pi/12 about point K. Line E is the reflection of line R across point P. Let J be the vecto... | 13.06 | MATH |
[
{
"content": "IX = 7. Let Y be the midpoint of segment XI. Let A be the rotation of point X by angle pi/3 around point I. Point J is the reflection of point X across point A. Point W is the midpoint of segment XA. Point Q is the reflection of point Y across segment IW. What is the measure of angle JWQ, in radia... | 1.05 | MATH |
[
{
"content": "LG = 4. Let O be the line through points L and G. Let T be the perpendicular bisector of segment GL. Point Z is the reflection of point L across point G. Let V be the reflection of line T through point G. Point E is the intersection of lines O and V. Find the distance between points Z and E. Expre... | 2.0 | MATH |
[
{
"content": "Let KA = 7. Let C be the midpoint of segment AK. Point Q is the reflection of point C across point A. Let U be the rotation of point K by angle 11pi/12 around point Q. Line H is the angle bisector of angle CAU. Line N is the reflection of line H across point C. Line Z is the perpendicular bisector... | 12.23 | MATH |
[
{
"content": "OD = 4. Point L is the reflection of point O across point D. Let E be the rotation of point D by angle pi/4 around point L. Point R is obtained by rotating point O by angle 5pi/6 about point D. Let Y be the rotation of point O by angle pi/2 around point D. Let J be the reflection of point O across... | 11.61 | MATH |
[
{
"content": "Let RJ = 11. Let X be the rotation of point J by angle 7pi/12 around point R. Let K be the line through points R and J. Point I is the reflection of point R across point J. Let M be the reflection of point R across point X. Line D passes through point R perpendicular to line K. Point E is the midp... | 19.15 | MATH |
[
{
"content": "Let HR = 11. Point M is obtained by rotating point H by angle pi/3 about point R. Point B is the reflection of point R across point M. Point Z is the midpoint of segment MB. Let P be the angle bisector of angle ZMR. Point C is obtained by rotating point Z by angle 7pi/12 about point R. Let D be th... | 89.11 | MATH |
[
{
"content": "VB = 6. Let H be the midpoint of segment BV. Line L is the perpendicular bisector of segment BH. Point Z lies on line L at distance 5 from point V. Let F be the midpoint of segment HV. Point U is the midpoint of segment FZ. Point E is the reflection of point V across point Z. Point T is the reflec... | 15.85 | MATH |
[
{
"content": "DG = 7. Point V is obtained by rotating point D by angle pi/6 about point G. Let Z be the reflection of point G across point V. Let S be the line through point Z perpendicular to segment VZ. Point J is the reflection of point D across segment VZ. Point T is the reflection of point D across line S.... | 12.47 | MATH |
[
{
"content": "IP = 4. Let T be the line through points P and I. Let L be the vector from point P to point I. Point V is the reflection of point I across point P. Line W is the perpendicular bisector of segment VP. Let J be point I translated by vector L. Line A is the reflection of line W across point J. Let U ... | 19.5 | MATH |
[
{
"content": "MN = 6. Let L be the midpoint of segment NM. Let X be the midpoint of segment LN. Let K be the reflection of point X across point L. Point W is the midpoint of segment NK. Find the distance between points W and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the ... | 2.25 | MATH |
[
{
"content": "OC = 1. Point P is the reflection of point C across point O. Point N is the midpoint of segment CO. Let K be the rotation of point P by angle 11pi/12 around point C. Let B be the angle bisector of angle NKC. Point L is the reflection of point P across line B. Let S be the reflection of point L acr... | 5.32 | MATH |
[
{
"content": "FX = 2. Let P be the rotation of point X by angle 7pi/12 around point F. Point V is the midpoint of segment FP. Let E be the rotation of point P by angle 7pi/12 around point V. Point N is the midpoint of segment FX. Let Y be the line through point E perpendicular to segment NE. Point H is the refl... | 2.77 | MATH |
[
{
"content": "WU = 11. Point M is the midpoint of segment WU. Let I be the perpendicular bisector of segment WM. Point P is the reflection of point M across point U. Point R is obtained by rotating point U by angle 2pi/3 about point W. Point K is the reflection of point P across line I. Let H be the reflection ... | 407.45 | MATH |
[
{
"content": "Let CD = 1. Let R be the reflection of point C across point D. Let W be the perpendicular bisector of segment RD. Let K be the reflection of line W through point R. Let G be the midpoint of segment CD. Point N is the midpoint of segment RG. Let O be the reflection of line W across line K. Line F i... | 14.09 | MATH |
[
{
"content": "ZJ = 11. Line T passes through point Z perpendicular to segment JZ. Point O is the midpoint of segment ZJ. Point A is the reflection of point O across line T. Let R be the midpoint of segment ZO. What is the distance between points R and A? Express your answer as a decimal number rounded to 2 deci... | 8.25 | MATH |
[
{
"content": "ZO = 7. Let N be the perpendicular bisector of segment OZ. Let M be the line through point O parallel to line N. Point X lies on line M at distance 8 from point Z. Point V is the midpoint of segment XO. Line Q is the reflection of line N across point X. Point W is the reflection of point V across ... | 10.63 | MATH |
[
{
"content": "SZ = 10. Point U is the midpoint of segment SZ. Let G be the line through point U perpendicular to segment ZU. Point T is the midpoint of segment ZU. Point E is the reflection of point T across line G. Find the distance between points E and U. Express your answer as a decimal number rounded to 2 d... | 2.5 | MATH |
[
{
"content": "Let AZ = 5. Point J is the midpoint of segment ZA. Let D be the reflection of point Z across point A. Let W be the midpoint of segment JD. Let S be the midpoint of segment ZJ. Find the distance between points S and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent ... | 5.0 | MATH |
[
{
"content": "NC = 2. Point I is obtained by rotating point N by angle pi/6 about point C. Point E is the reflection of point C across point I. Let L be the perpendicular bisector of segment EI. Let Z be the midpoint of segment EI. Let B be the perpendicular bisector of segment NE. Let M be the line through poi... | 2.2 | MATH |
[
{
"content": "CW = 3. Let A be the rotation of point C by angle 5pi/12 around point W. Let R be the rotation of point A by angle pi around point C. Let D be the vector from point W to point R. Let F be the midpoint of segment WA. Let B be point C translated by vector D. Let K be the perpendicular bisector of se... | 13.2 | MATH |
[
{
"content": "PH = 5. Let O be the midpoint of segment PH. Point W is obtained by rotating point P by angle pi/3 about point H. Point K is the reflection of point W across point P. Point R is the reflection of point W across point O. Point Z is the reflection of point O across point H. Let L be the angle bisect... | 16.57 | MATH |
[
{
"content": "Let VT = 5. Let E be the rotation of point V by angle pi around point T. Point I is the midpoint of segment TV. Let H be the line through point I perpendicular to segment EI. Point G is the reflection of point E across line H. Point Q is the midpoint of segment EI. Find the distance between points... | 11.25 | MATH |
[
{
"content": "Let DP = 2. Point F is the reflection of point P across point D. Let X be the reflection of point D across point F. Let U be the midpoint of segment FX. Line J is the perpendicular bisector of segment PU. Point M is the reflection of point X across line J. What is the distance between points M and... | 5.0 | MATH |
[
{
"content": "NT = 4. Let J be the midpoint of segment NT. Let Z be the reflection of point J across point T. Let L be the perpendicular bisector of segment NT. Line U is the perpendicular bisector of segment ZT. Let F be the rotation of point N by angle 5pi/12 around point T. Let O be the rotation of point J b... | 1.9 | MATH |
[
{
"content": "Let BL = 2. Let X be the reflection of point B across point L. Let Y be the line through points L and X. Line K passes through point L perpendicular to line Y. Point V lies on line K at distance 5 from point L. Let M be the midpoint of segment BV. Point Q is the reflection of point B across point ... | 14.81 | MATH |
[
{
"content": "Let OF = 5. Let M be the rotation of point F by angle 2pi/3 around point O. Let R be the midpoint of segment OM. Point Y is the midpoint of segment RO. Point N is the midpoint of segment FR. Point X is the reflection of point Y across segment FR. Find the length of segment NX. Express your answer ... | 2.5 | MATH |
[
{
"content": "Let KV = 4. Let F be the vector from point K to point V. Point R is the translation of point V by vector F. Point M is obtained by rotating point K by angle pi/3 about point V. Line O passes through point M perpendicular to segment KV. Let Q be the reflection of point K across point R. Line P is t... | 41.84 | MATH |
[
{
"content": "PG = 2. Let E be the vector from point G to point P. Point V is obtained by rotating point G by angle 7pi/12 about point P. Let F be the reflection of point G across point P. Point T is the reflection of point G across point V. Let N be the reflection of point V across point T. Point U is the tran... | 4.91 | MATH |
[
{
"content": "Let HI = 11. Line R passes through point I perpendicular to segment IH. Point N is the reflection of point H across line R. Point B is obtained by rotating point H by angle pi about point N. Let V be the rotation of point B by angle 2pi/3 around point I. Let J be the line through point N parallel ... | 126.86 | MATH |
[
{
"content": "RE = 9. Line X passes through points E and R. Let A be the rotation of point E by angle pi/4 around point R. Let Y be the rotation of point A by angle pi/6 around point R. Point L is the midpoint of segment YE. Point C is the reflection of point E across point R. Let P be the midpoint of segment L... | 16.76 | MATH |
[
{
"content": "PV = 10. Let C be the line through points V and P. Let F be the line through point V perpendicular to line C. Let K be the reflection of point V across point P. Point R is the midpoint of segment VP. Point X is the reflection of point R across line F. What is the distance between points X and K? E... | 25.0 | MATH |
[
{
"content": "Let ZX = 5. Let J be the perpendicular bisector of segment XZ. Line S is the reflection of line J across point Z. Point I is the reflection of point X across line S. Line T is the reflection of line S across line J. Let O be the midpoint of segment ZI. Point Y lies on line S at distance 1 from poi... | 120.43 | MATH |
[
{
"content": "VH = 9. Point Q is the reflection of point H across point V. Let B be the rotation of point Q by angle pi/4 around point H. Let S be the rotation of point B by angle 2pi/3 around point V. Let Y be the rotation of point H by angle pi/2 around point S. Point K is obtained by rotating point V by angl... | 10.21 | MATH |
[
{
"content": "MV = 3. Let I be the rotation of point M by angle 3pi/4 around point V. Let K be the reflection of point I across point M. Point N is the midpoint of segment KM. Point Y is the reflection of point N across point K. Let X be the perpendicular bisector of segment NM. Line R is the reflection of line... | 22.17 | MATH |
[
{
"content": "AF = 1. Let Y be the rotation of point F by angle 3pi/4 around point A. Point L is obtained by rotating point A by angle pi/12 about point Y. Line I is the perpendicular bisector of segment LY. Line J is the angle bisector of angle YFL. Line U is the reflection of line J across line I. Line X pass... | 1.19 | MATH |
[
{
"content": "Let RX = 5. Let Y be the rotation of point X by angle pi/2 around point R. Point F is obtained by rotating point R by angle pi/3 about point X. Point S is the reflection of point Y across point R. Let T be the vector from point R to point F. Line Q passes through points Y and X. Let G be the refle... | 23.59 | MATH |
[
{
"content": "BK = 9. Let Z be the perpendicular bisector of segment KB. Let R be the midpoint of segment KB. Let E be the reflection of point R across point B. Line Y passes through point K parallel to line Z. Point M is obtained by rotating point B by angle 5pi/12 about point K. Point V is the reflection of p... | 19.51 | MATH |
[
{
"content": "BQ = 3. Let I be the midpoint of segment QB. Point G is obtained by rotating point B by angle 5pi/12 about point I. Let Z be the midpoint of segment BI. Let D be the angle bisector of angle IBZ. Point J is obtained by rotating point Q by angle 5pi/12 about point I. Line O is the perpendicular bise... | 3.65 | MATH |
[
{
"content": "Let YK = 3. Line L is the perpendicular bisector of segment YK. Point M is obtained by rotating point Y by angle pi/2 about point K. Let W be the rotation of point M by angle pi/12 around point Y. Point S is the reflection of point K across point W. Point H is the reflection of point W across line... | 1.51 | MATH |
[
{
"content": "Let GW = 6. Let N be the vector from point W to point G. Point J is obtained by rotating point W by angle 3pi/4 about point G. Let P be point J translated by vector N. Let L be the midpoint of segment WJ. Line O is the angle bisector of angle JGW. Let R be the reflection of line O through point P.... | 6.0 | MATH |
[
{
"content": "PO = 6. Let K be the reflection of point O across point P. Point Z is obtained by rotating point P by angle 11pi/12 about point K. Let T be the line through points Z and P. Let B be the reflection of line T through point K. Let Y be the reflection of line B across line T. Let C be the reflection o... | 13.25 | MATH |
[
{
"content": "Let PU = 9. Line R is the perpendicular bisector of segment PU. Let E be the reflection of line R through point U. Let J be the rotation of point U by angle pi around point P. Point G is the reflection of point J across line E. Let N be the reflection of point G across point U. Point Y is the refl... | 85.5 | MATH |
[
{
"content": "FP = 10. Let Z be the rotation of point P by angle pi/3 around point F. Point B is the reflection of point P across point Z. Point S is the midpoint of segment FB. Point W is the midpoint of segment PZ. Let L be the midpoint of segment SP. Let Y be the reflection of point W across point F. Point C... | 8.3 | MATH |
[
{
"content": "Let NR = 9. Let T be the rotation of point N by angle 2pi/3 around point R. Point V is the reflection of point T across segment NR. Line O passes through points V and T. Point Y is the reflection of point N across line O. Line U passes through point Y parallel to line O. Let C be the reflection of... | 82.49 | MATH |
[
{
"content": "YX = 12. Let D be the reflection of point X across point Y. Let J be the rotation of point D by angle pi around point X. Let F be the reflection of point Y across point J. Point A is obtained by rotating point F by angle 5pi/6 about point Y. Let O be the rotation of point A by angle pi around poin... | 98.66 | MATH |
[
{
"content": "HV = 11. Let R be the rotation of point V by angle pi/2 around point H. Let Z be the rotation of point R by angle pi around point V. Let A be the reflection of point H across point V. Let S be the perpendicular bisector of segment VH. Let C be the reflection of point V across point Z. Point E is t... | 22.21 | MATH |
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