messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let ST = 7. Point F is the midpoint of segment ST. Line R is the perpendicular bisector of segment TF. Point B is the reflection of point S across line R. Let I be the rotation of point B by angle 3pi/4 around point F. Line U is the reflection of line R across point S. Let O be the midpoint of seg... | 16.51 | MATH |
[
{
"content": "Let MU = 10. Let V be the rotation of point M by angle 2pi/3 around point U. Point S is obtained by rotating point U by angle pi about point V. Let R be the midpoint of segment VU. Let Z be the rotation of point R by angle 11pi/12 around point S. Line H is the perpendicular bisector of segment RS.... | 28.21 | MATH |
[
{
"content": "GY = 2. Point Z is the midpoint of segment GY. Point S is obtained by rotating point G by angle pi about point Y. Let D be the perpendicular bisector of segment SY. Line R is the reflection of line D across point Y. Let O be the rotation of point Z by angle 2pi/3 around point S. Let X be the vecto... | 4.91 | MATH |
[
{
"content": "IC = 3. Let L be the reflection of point C across point I. Let U be the rotation of point L by angle 2pi/3 around point I. Line K is the perpendicular bisector of segment LU. Let D be the midpoint of segment UC. Point E is the reflection of point D across segment IC. Point O is the reflection of p... | 4.5 | MATH |
[
{
"content": "LO = 9. Let H be the midpoint of segment OL. Point J is the midpoint of segment LH. Let W be the reflection of point O across point L. Point U is the reflection of point O across point W. Point C is the midpoint of segment OJ. Point R is the reflection of point J across point L. Let V be the perpe... | 72.0 | MATH |
[
{
"content": "QN = 3. Line U passes through points N and Q. Point E is obtained by rotating point N by angle pi/6 about point Q. Point J is the reflection of point E across line U. Point P is obtained by rotating point J by angle 11pi/12 about point N. Line V is the perpendicular bisector of segment JP. Point S... | 5.93 | MATH |
[
{
"content": "IC = 3. Point K is the midpoint of segment IC. Let S be the midpoint of segment CK. Point N is obtained by rotating point K by angle pi/6 about point C. Let L be the reflection of point C across point N. Let V be the rotation of point S by angle 3pi/4 around point L. Let M be the reflection of poi... | 4.09 | MATH |
[
{
"content": "RK = 2. Line F is the perpendicular bisector of segment KR. Point E is obtained by rotating point R by angle pi/3 about point K. Line Z passes through points E and K. Point Y lies on line Z. Point J is the midpoint of segment YK. Let W be the perpendicular bisector of segment YK. Line U is the ref... | 7.21 | MATH |
[
{
"content": "Let VW = 1. Point A is obtained by rotating point W by angle 11pi/12 about point V. Line E is the perpendicular bisector of segment AV. Point Y is obtained by rotating point V by angle 5pi/6 about point A. Line G is the angle bisector of angle YVW. Line L is the reflection of line G across line E.... | 0.34 | MATH |
[
{
"content": "Let HM = 11. Let E be the perpendicular bisector of segment HM. Point Z lies on line E at distance 5 from point M. Let P be the reflection of point Z across point H. Let T be the midpoint of segment ZM. Line J passes through points M and Z. Point Q is the reflection of point P across point T. Poin... | 29.6 | MATH |
[
{
"content": "Let VG = 5. Line N is the perpendicular bisector of segment VG. Point Z is the reflection of point G across point V. Let I be the rotation of point V by angle pi/2 around point G. Let O be the line through point I perpendicular to line N. Line T is the reflection of line N across point I. Line D i... | 44.0 | MATH |
[
{
"content": "Let MB = 8. Let A be the rotation of point B by angle pi/12 around point M. Point T is obtained by rotating point A by angle 3pi/4 about point M. Let E be the rotation of point A by angle pi/12 around point M. Let O be the perpendicular bisector of segment TM. Point F is the reflection of point E ... | 21.17 | MATH |
[
{
"content": "HZ = 9. Point J is obtained by rotating point Z by angle pi/4 about point H. Let E be the rotation of point Z by angle 11pi/12 around point J. Let T be the line through points H and E. Point W is the reflection of point J across line T. Let A be the line through point W parallel to line T. Let I b... | 15.85 | MATH |
[
{
"content": "ZT = 2. Point B is the reflection of point Z across point T. Let W be the reflection of point Z across point B. Line A is the perpendicular bisector of segment ZB. Point V is the reflection of point W across line A. Point Y is on line A with |YV| = 9. Line H is the perpendicular bisector of segmen... | 15.0 | MATH |
[
{
"content": "XZ = 4. Point O is obtained by rotating point X by angle 5pi/6 about point Z. Let V be the midpoint of segment XZ. Point U is obtained by rotating point Z by angle 3pi/4 about point O. Let B be the angle bisector of angle XUZ. Point T is the reflection of point X across point Z. Let E be the refle... | 10.67 | MATH |
[
{
"content": "Let CR = 4. Line M is the perpendicular bisector of segment RC. Point I is obtained by rotating point C by angle 3pi/4 about point R. Point P is the midpoint of segment RI. Line B passes through point I parallel to line M. Point E is obtained by rotating point I by angle 7pi/12 about point P. Let ... | 2.31 | MATH |
[
{
"content": "Let XK = 4. Let R be the line through points X and K. Let G be the line through point X perpendicular to line R. Point J is the reflection of point K across line G. Let B be the reflection of line G through point K. Point N is the reflection of point J across line B. Let F be the midpoint of segme... | 10.0 | MATH |
[
{
"content": "Let ZF = 9. Point X is the midpoint of segment ZF. Point Q is the midpoint of segment FX. Point U is the midpoint of segment QX. Let V be the rotation of point F by angle 5pi/12 around point Z. Point E is obtained by rotating point V by angle pi/4 about point U. Point Y is the midpoint of segment ... | 6.0 | MATH |
[
{
"content": "Let KL = 6. Point M is obtained by rotating point K by angle pi/4 about point L. Point W is the midpoint of segment LK. Point D is the midpoint of segment MK. Point V is the midpoint of segment WD. Point O is the reflection of point V across segment LK. Let S be the reflection of point L across po... | 5.16 | MATH |
[
{
"content": "RX = 4. Let L be the reflection of point R across point X. Line K is the angle bisector of angle RXL. Point C is obtained by rotating point L by angle pi/12 about point X. Line I passes through point C parallel to line K. Point O is obtained by rotating point L by angle 7pi/12 about point R. Let A... | 10.5 | MATH |
[
{
"content": "Let FX = 11. Let G be the perpendicular bisector of segment XF. Point V is the reflection of point F across point X. Point O lies on line G at distance 11 from point X. Line B is the perpendicular bisector of segment XV. Point Z is the reflection of point X across point O. Point Q is the reflectio... | 59.24 | MATH |
[
{
"content": "Let RW = 9. Let Q be the reflection of point W across point R. Point B is the midpoint of segment WR. Point I is the midpoint of segment BW. Point K is the midpoint of segment RB. Let L be the midpoint of segment KQ. What is the distance between points L and I? Express your answer as a decimal num... | 10.12 | MATH |
[
{
"content": "Let XV = 12. Point K is obtained by rotating point X by angle pi about point V. Let L be the perpendicular bisector of segment KV. Point C lies on line L at distance 7 from point K. Line F passes through point C perpendicular to line L. Point O is the reflection of point C across segment XV. Let Y... | 9.22 | MATH |
[
{
"content": "WV = 1. Let N be the midpoint of segment WV. Line T is the angle bisector of angle WNV. Point B is on line T with |BN| = 3. Point C is the reflection of point B across segment WV. Let X be the reflection of point B across point C. Point J is the midpoint of segment WX. Point F is the reflection of... | 9.12 | MATH |
[
{
"content": "BA = 4. Let W be the line through point B perpendicular to segment BA. Point L is obtained by rotating point A by angle 5pi/6 about point B. Line T passes through point L perpendicular to segment BA. Let P be the reflection of line W through point A. Line Q is the angle bisector of angle BLA. Line... | 2.62 | MATH |
[
{
"content": "Let ZL = 10. Point J is obtained by rotating point L by angle 2pi/3 about point Z. Point R is the reflection of point Z across point J. Let Q be the perpendicular bisector of segment ZR. Point O is the reflection of point L across point R. Let W be the reflection of line Q through point O. Point I... | 153.95 | MATH |
[
{
"content": "AN = 7. Let P be the midpoint of segment NA. Point F is the midpoint of segment NP. Point K is the midpoint of segment FP. Let V be the line through point A perpendicular to segment PN. Let X be the midpoint of segment KP. Line E is the angle bisector of angle APX. Point R is the reflection of poi... | 7.0 | MATH |
[
{
"content": "GN = 9. Line M is the perpendicular bisector of segment GN. Line V passes through points N and G. Point C lies on line M at distance 9 from point N. Let D be the rotation of point G by angle 7pi/12 around point C. Point T is the reflection of point D across line V. Point S is the reflection of poi... | 10.06 | MATH |
[
{
"content": "QN = 9. Point Y is the midpoint of segment NQ. Let Z be the rotation of point Q by angle pi/3 around point Y. Line M passes through point Q parallel to segment ZY. Let W be the reflection of point N across point Z. Point D is the reflection of point Y across point W. Let O be the rotation of point... | 26.6 | MATH |
[
{
"content": "Let VY = 9. Point P is the reflection of point Y across point V. Point J is obtained by rotating point P by angle 11pi/12 about point Y. Let W be the perpendicular bisector of segment JP. Point X is obtained by rotating point V by angle 3pi/4 about point J. Let F be the line through points J and Y... | 6.6 | MATH |
[
{
"content": "VC = 6. Point T is the midpoint of segment VC. Point E is the midpoint of segment TV. Point D is the reflection of point E across point C. Point R is the reflection of point C across point V. Let X be the midpoint of segment ET. Point B is the reflection of point D across point R. What is the dist... | 24.75 | MATH |
[
{
"content": "Let ZS = 7. Let N be the vector from point Z to point S. Let D be the midpoint of segment ZS. Let F be the angle bisector of angle SDZ. Line T is the reflection of line F across point S. Line W is the reflection of line F across point Z. Point L lies on line T at distance 9 from point Z. Let M be ... | 2.38 | MATH |
[
{
"content": "KD = 10. Let N be the rotation of point K by angle 5pi/6 around point D. Let F be the rotation of point K by angle pi/4 around point D. Point X is the reflection of point N across point D. Point V is the midpoint of segment FX. Point E is the midpoint of segment XD. Line Q passes through point F p... | 9.94 | MATH |
[
{
"content": "IC = 2. Point P is the midpoint of segment CI. Line F passes through points P and C. Let Z be the line through point P perpendicular to line F. Point A is on line F with |AI| = 5. Let K be the vector from point I to point A. Line L passes through point I parallel to line Z. Point X is on line L wi... | 20.0 | MATH |
[
{
"content": "Let BQ = 8. Line K passes through points B and Q. Point A is the midpoint of segment BQ. Point N lies on line K at distance 9 from point B. Point X is on line K. Let V be the rotation of point N by angle pi/3 around point X. Let M be the midpoint of segment VB. Let T be the midpoint of segment AV.... | 2.0 | MATH |
[
{
"content": "JT = 9. Point D is obtained by rotating point T by angle pi/12 about point J. Let R be the vector from point J to point T. Let N be point T translated by vector R. Point H is the midpoint of segment JD. Point M is the midpoint of segment HD. Point C is the midpoint of segment HN. Let K be the refl... | 11.61 | MATH |
[
{
"content": "UK = 11. Let H be the midpoint of segment UK. Let A be the rotation of point H by angle pi/3 around point U. Let X be the vector from point U to point A. Point O is the reflection of point K across point U. Let D be point H translated by vector X. Let G be the line through points U and D. Point J ... | 36.91 | MATH |
[
{
"content": "Let TZ = 9. Point I is obtained by rotating point T by angle pi/6 about point Z. Let D be the midpoint of segment ZT. Let H be the rotation of point D by angle pi/4 around point Z. Let K be the midpoint of segment DI. Let R be the midpoint of segment TI. Line P is the perpendicular bisector of seg... | 12.3 | MATH |
[
{
"content": "Let GZ = 8. Let J be the midpoint of segment GZ. Let D be the angle bisector of angle JZG. W is placed 9 units away from Z. Let L be the angle bisector of angle GJW. Point K lies on line L at distance 4 from point J. Point P is the reflection of point K across line D. Point A is the reflection of ... | 4.0 | MATH |
[
{
"content": "Let PF = 3. Point K is the reflection of point P across point F. Point V is obtained by rotating point K by angle 7pi/12 about point P. Point E is obtained by rotating point K by angle 11pi/12 about point P. Let O be the perpendicular bisector of segment EV. Let N be the reflection of line O throu... | 14.16 | MATH |
[
{
"content": "Let RE = 6. Point I is the midpoint of segment ER. Let L be the midpoint of segment RI. Line J is the perpendicular bisector of segment LE. Let D be the midpoint of segment RL. Point C is the midpoint of segment LD. Let S be the reflection of point C across point D. Point O is the midpoint of segm... | 5.05 | MATH |
[
{
"content": "XK = 6. Let W be the rotation of point X by angle pi/2 around point K. Let A be the midpoint of segment XK. Point Z is the reflection of point A across point K. Point I is the reflection of point K across point W. Let S be the reflection of point K across point Z. Find the distance between points ... | 13.42 | MATH |
[
{
"content": "Let WE = 6. Let S be the rotation of point E by angle 5pi/12 around point W. Line G passes through point S perpendicular to segment SW. Let C be the line through point E parallel to line G. Let P be the reflection of point W across point S. Point Q is the midpoint of segment SE. Point J is the ref... | 4.82 | MATH |
[
{
"content": "Let AJ = 5. Let H be the rotation of point A by angle 5pi/12 around point J. Let Q be the reflection of point J across point H. Let I be the line through point H parallel to segment AQ. Let K be the perpendicular bisector of segment AQ. Point S is the reflection of point J across line I. Let R be ... | 7.27 | MATH |
[
{
"content": "Let NB = 1. Point Y is the midpoint of segment NB. Let V be the reflection of point B across point N. Line Q is the perpendicular bisector of segment YV. Point I is the reflection of point B across line Q. Point F is the midpoint of segment VI. What is the distance between points N and F? Express ... | 1.25 | MATH |
[
{
"content": "EG = 4. Let O be the midpoint of segment GE. Let Q be the rotation of point G by angle 5pi/12 around point E. Let B be the rotation of point E by angle pi around point Q. Let D be the midpoint of segment QE. Let S be the perpendicular bisector of segment GO. Point P lies on line S. Line M passes t... | 8.03 | MATH |
[
{
"content": "Let IK = 8. Point J is obtained by rotating point K by angle pi/3 about point I. Point E is obtained by rotating point J by angle pi about point I. Line B is the perpendicular bisector of segment IE. Point G is on line B with |GJ| = 12. Point Q is the reflection of point G across segment IE. Point... | 4.0 | MATH |
[
{
"content": "EA = 3. Let S be the perpendicular bisector of segment AE. Line I is the reflection of line S across point E. Point D lies on line I. Line Y is the reflection of line S across point D. Point H is the reflection of point D across line Y. Find the distance between points H and D. Express your answer... | 6.0 | MATH |
[
{
"content": "RS = 2. Point E is the reflection of point R across point S. Point Q is the reflection of point S across point R. Let Y be the angle bisector of angle SRQ. Let H be the angle bisector of angle ESQ. Let Z be the reflection of line Y through point Q. Let X be the midpoint of segment QE. Line K passe... | 5.51 | MATH |
[
{
"content": "Let BW = 10. Let T be the rotation of point W by angle pi/4 around point B. Point Q is the reflection of point W across point T. Line N passes through points Q and B. Line P passes through point T perpendicular to line N. Point R is the reflection of point Q across line P. Find the length of segme... | 7.65 | MATH |
[
{
"content": "AK = 12. Point D is the midpoint of segment KA. Line W is the perpendicular bisector of segment KD. Point R is the reflection of point A across line W. Let S be the rotation of point D by angle 2pi/3 around point R. Let H be the angle bisector of angle RSA. Line O passes through point A perpendicu... | 9.03 | MATH |
[
{
"content": "Let LK = 10. Point A is obtained by rotating point L by angle 2pi/3 about point K. Line B is the perpendicular bisector of segment LK. Let S be the midpoint of segment LA. Let M be the reflection of point S across point A. Point P is the reflection of point A across line B. Point R is the reflecti... | 28.23 | MATH |
[
{
"content": "NF = 11. Let W be the line through point N perpendicular to segment NF. Line H is the perpendicular bisector of segment NF. Point Y is on line W with |YF| = 1. Let V be the midpoint of segment NF. Line E is the reflection of line W across line H. Point D is the midpoint of segment VF. Line A passe... | 8.31 | MATH |
[
{
"content": "NS = 6. Let G be the rotation of point N by angle pi/12 around point S. Let P be the midpoint of segment NS. Point D is the reflection of point G across segment NS. Let X be the rotation of point N by angle 3pi/4 around point D. Let R be the line through point X perpendicular to segment NS. Let J ... | 3.6 | MATH |
[
{
"content": "Let NJ = 8. Point L is obtained by rotating point J by angle pi/2 about point N. Point Y is the reflection of point J across point N. Line M is the perpendicular bisector of segment YJ. Let T be the reflection of point N across point J. Point V lies on line M. Point W lies on line M at distance 12... | 7.21 | MATH |
[
{
"content": "IK = 1. B is placed 1 units away from K. Point U is obtained by rotating point B by angle 7pi/12 about point K. Let L be the rotation of point B by angle 3pi/4 around point K. Point M is obtained by rotating point U by angle 7pi/12 about point L. Point W is the midpoint of segment MK. Let Z be the... | 0.87 | MATH |
[
{
"content": "JR = 1. Line Z is the perpendicular bisector of segment JR. Let E be the vector from point J to point R. Point K is the midpoint of segment RJ. Let T be point R translated by vector E. Let I be the line through point J parallel to line Z. Let N be the perpendicular bisector of segment KT. Let F be... | 2.47 | MATH |
[
{
"content": "LV = 6. Let R be the reflection of point L across point V. Let N be the reflection of point V across point L. Let X be the rotation of point L by angle pi around point R. Line J is the perpendicular bisector of segment LN. Point H is the midpoint of segment VX. Let Z be the reflection of point L a... | 15.92 | MATH |
[
{
"content": "KM = 8. Point A is the midpoint of segment KM. Point C is the reflection of point A across point K. Point R is the reflection of point C across point A. Point O is obtained by rotating point A by angle pi/4 about point M. Let Z be the rotation of point C by angle 7pi/12 around point A. Let G be th... | 20.97 | MATH |
[
{
"content": "Let BM = 1. Point P is the midpoint of segment MB. Point F is obtained by rotating point B by angle 3pi/4 about point M. Let H be the rotation of point P by angle pi/12 around point M. Let K be the perpendicular bisector of segment FB. Point L is the reflection of point H across line K. Point Y is... | 0.79 | MATH |
[
{
"content": "Let GX = 10. Let O be the perpendicular bisector of segment GX. J is constructed so that XJ = 9. Let S be the midpoint of segment JX. Let K be the line through points S and G. Let P be the reflection of point G across point S. Line V is the reflection of line O across line K. Line Y passes through... | 10.0 | MATH |
[
{
"content": "NJ = 2. Let Q be the perpendicular bisector of segment JN. Line I is the reflection of line Q across point N. Point C is the reflection of point J across point N. Let D be the vector from point C to point J. Let R be point J translated by vector D. Let W be the reflection of line I across line Q. ... | 14.0 | MATH |
[
{
"content": "Let MS = 11. Point P is obtained by rotating point S by angle 5pi/6 about point M. Let V be the line through points P and M. Let I be the midpoint of segment SM. Let O be the midpoint of segment SI. Let N be the angle bisector of angle MPI. Line A is the reflection of line N across point I. Point ... | 50.32 | MATH |
[
{
"content": "Let WH = 1. Line T is the perpendicular bisector of segment HW. Point K is the midpoint of segment WH. Point I is obtained by rotating point W by angle pi/12 about point K. Line E passes through points I and H. Line C is the reflection of line E across point K. Point M is the reflection of point H... | 1.0 | MATH |
[
{
"content": "PB = 6. Let N be the perpendicular bisector of segment BP. Point I lies on line N at distance 1 from point P. Point A lies on line N at distance 4 from point B. Let K be the midpoint of segment BA. Let L be the midpoint of segment AI. Line M passes through point L perpendicular to line N. Point S ... | 1.0 | MATH |
[
{
"content": "Let VG = 2. Line C is the perpendicular bisector of segment VG. Let O be the midpoint of segment GV. Line X is the reflection of line C across point G. Point Z is obtained by rotating point V by angle 11pi/12 about point G. Let T be the reflection of line X across line C. Line P is the reflection ... | 3.0 | MATH |
[
{
"content": "BA = 3. Point D is obtained by rotating point B by angle 2pi/3 about point A. Let K be the perpendicular bisector of segment AB. Let E be the line through points B and A. Let V be the reflection of line K through point D. Lines E and V intersect at point Z. What is the distance between points B an... | 7.5 | MATH |
[
{
"content": "Let ET = 6. Point C is obtained by rotating point E by angle 11pi/12 about point T. Line V is the perpendicular bisector of segment EC. Let S be the reflection of line V through point E. Let O be the reflection of point E across point T. Point G is the reflection of point O across line S. Point P ... | 32.74 | MATH |
[
{
"content": "Let CV = 5. Let L be the midpoint of segment CV. Let J be the midpoint of segment VL. Let A be the rotation of point L by angle 3pi/4 around point V. Point T is the reflection of point C across point A. Point B is obtained by rotating point J by angle 5pi/6 about point C. Let E be the rotation of ... | 18.2 | MATH |
[
{
"content": "Let HI = 9. Let M be the reflection of point I across point H. Let C be the reflection of point I across point M. Point K is the reflection of point H across point C. Let V be the vector from point H to point I. Point N is obtained by rotating point M by angle 3pi/4 about point K. Let U be point N... | 65.33 | MATH |
[
{
"content": "JW = 10. Point H is the reflection of point W across point J. Let L be the reflection of point W across point H. Let S be the line through points L and J. Line M passes through point H perpendicular to line S. Let N be the rotation of point J by angle 3pi/4 around point L. Let Z be the reflection ... | 361.84 | MATH |
[
{
"content": "AC = 1. Let N be the reflection of point A across point C. Point I is the reflection of point N across point A. Point D is the midpoint of segment AI. Let W be the rotation of point A by angle 3pi/4 around point D. Let X be the rotation of point W by angle 7pi/12 around point N. Let L be the midpo... | 0.5 | MATH |
[
{
"content": "IE = 4. Point A is obtained by rotating point I by angle 11pi/12 about point E. Let P be the midpoint of segment EA. Let K be the angle bisector of angle PAI. Line W passes through point I parallel to line K. Point B is the reflection of point P across line W. Let D be the midpoint of segment IP. ... | 15.04 | MATH |
[
{
"content": "Let EO = 3. Let H be the rotation of point O by angle 5pi/6 around point E. Let J be the rotation of point O by angle 3pi/4 around point H. Let F be the vector from point H to point O. Let S be point E translated by vector F. Let X be the rotation of point S by angle 5pi/6 around point J. Line Y i... | 39.09 | MATH |
[
{
"content": "FS = 9. Point V is the midpoint of segment SF. Let C be the perpendicular bisector of segment SV. Line Y is the reflection of line C across point S. Point O is the reflection of point F across line Y. Find the distance between points O and V. Express your answer as a decimal number rounded to 2 de... | 18.0 | MATH |
[
{
"content": "SN = 6. Let P be the vector from point S to point N. Let A be point N translated by vector P. Point Y is obtained by rotating point N by angle 5pi/12 about point A. Let W be the reflection of point N across point S. Point R is the midpoint of segment AY. Let O be the midpoint of segment AR. Line F... | 8.29 | MATH |
[
{
"content": "OK = 9. Point X is the reflection of point K across point O. Point Q is obtained by rotating point X by angle pi/6 about point O. Let M be the perpendicular bisector of segment XQ. Line S passes through point O perpendicular to line M. Point N is the midpoint of segment OK. Let I be the line throu... | 4.66 | MATH |
[
{
"content": "OT = 1. Point E is the midpoint of segment TO. Let H be the vector from point E to point O. Point A is the midpoint of segment OE. Line F is the perpendicular bisector of segment TO. Line C is the reflection of line F across point O. Point W is the midpoint of segment TE. Let I be the reflection o... | 7.75 | MATH |
[
{
"content": "XQ = 7. Point P is the reflection of point Q across point X. Let R be the rotation of point X by angle 5pi/12 around point P. Point U is the midpoint of segment QR. Line B is the perpendicular bisector of segment QX. Line F is the reflection of line B across point X. Let V be the perpendicular bis... | 17.44 | MATH |
[
{
"content": "MW = 4. Let N be the rotation of point W by angle pi/6 around point M. Let U be the line through points M and N. Let F be the rotation of point M by angle pi/3 around point W. Line D passes through points M and W. Line A is the reflection of line U across line D. Let O be the reflection of point F... | 26.32 | MATH |
[
{
"content": "Let OM = 9. Let X be the reflection of point M across point O. Let F be the line through points M and X. Point N is on line F. Let J be the rotation of point O by angle 7pi/12 around point X. Let Q be the reflection of point M across point N. Point W is the reflection of point Q across point J. Po... | 20.75 | MATH |
[
{
"content": "YU = 6. Let S be the line through points U and Y. Let X be the rotation of point U by angle pi/4 around point Y. Line W is the perpendicular bisector of segment YX. Line T is the reflection of line W across point Y. Let D be the line through point U perpendicular to line S. Line I is the reflectio... | 12.6 | MATH |
[
{
"content": "Let GQ = 1. Let O be the vector from point Q to point G. Let J be the line through points G and Q. Let R be the midpoint of segment QG. Let S be point R translated by vector O. Let L be the perpendicular bisector of segment QG. Point Z is obtained by rotating point R by angle 2pi/3 about point G. ... | 0.58 | MATH |
[
{
"content": "Let ZP = 5. Let C be the midpoint of segment ZP. Line F passes through point P perpendicular to segment ZP. Point M is obtained by rotating point C by angle pi/6 about point P. Point N is the reflection of point C across point Z. Point L is the reflection of point Z across line F. Line Q passes th... | 12.23 | MATH |
[
{
"content": "Let TY = 1. Line A passes through points Y and T. Point V is the reflection of point T across point Y. Line U passes through point T perpendicular to line A. Point K is the reflection of point Y across line U. Find the distance between points V and K. Express your answer as a decimal number rounde... | 3.0 | MATH |
[
{
"content": "Let KH = 9. Point A is obtained by rotating point H by angle 11pi/12 about point K. Point L is the reflection of point K across point A. Point S is obtained by rotating point L by angle pi/12 about point K. Let M be the rotation of point K by angle pi/6 around point S. Let V be the reflection of p... | 53.79 | MATH |
[
{
"content": "IU = 12. Let T be the midpoint of segment UI. Line Z passes through points U and T. Let F be the rotation of point U by angle 2pi/3 around point I. Let P be the midpoint of segment IT. Point E is on line Z with |EP| = 2. Point Y is the reflection of point T across point I. Line O is the perpendicu... | 13.75 | MATH |
[
{
"content": "Let LO = 6. Let S be the reflection of point L across point O. Point R is the midpoint of segment OL. Line X is the perpendicular bisector of segment SO. Point A is on line X with |AO| = 9. Line M passes through points A and R. Line U passes through point R perpendicular to line M. Let B be the mi... | 4.5 | MATH |
[
{
"content": "OV = 10. Let G be the reflection of point V across point O. Point T is obtained by rotating point O by angle 2pi/3 about point G. Line U is the angle bisector of angle GTV. Point Q is the reflection of point T across point G. Line X is the reflection of line U across point Q. Point W is the reflec... | 8.87 | MATH |
[
{
"content": "Let XP = 6. Let Y be the perpendicular bisector of segment XP. Point W is obtained by rotating point P by angle 7pi/12 about point X. Let G be the reflection of line Y through point P. Let Z be the reflection of point X across point W. Point E is the midpoint of segment PW. Point R is the reflecti... | 10.2 | MATH |
[
{
"content": "Let CF = 5. Point U is the reflection of point C across point F. Let J be the perpendicular bisector of segment CF. Point W is the reflection of point U across point C. Point X is on line J with |XU| = 12. Let Y be the line through points C and X. Point G is the reflection of point U across line Y... | 15.99 | MATH |
[
{
"content": "Let HO = 3. Point K is obtained by rotating point H by angle pi/12 about point O. Point Z is the reflection of point H across segment OK. Let F be the rotation of point O by angle pi/12 around point K. Let L be the angle bisector of angle ZKO. Let Y be the midpoint of segment ZH. Let P be the refl... | 2.02 | MATH |
[
{
"content": "Let BL = 8. Point I is the reflection of point B across point L. Let X be the angle bisector of angle ILB. Line W is the perpendicular bisector of segment LB. Point F is the midpoint of segment IL. Point H is obtained by rotating point B by angle 2pi/3 about point L. Let Q be the line through poin... | 39.4 | MATH |
[
{
"content": "EB = 10. Let Z be the vector from point E to point B. Let F be the vector from point B to point E. Line T passes through points B and E. Let V be the vector from point E to point B. Point U is the reflection of point E across point B. Let Y be the rotation of point U by angle 5pi/12 around point B... | 52.99 | MATH |
[
{
"content": "RZ = 7. Let K be the reflection of point R across point Z. Point J is the reflection of point Z across point R. Point W is the midpoint of segment JK. Let A be the rotation of point J by angle pi/12 around point Z. Point D is the midpoint of segment RJ. Point G is obtained by rotating point D by a... | 27.35 | MATH |
[
{
"content": "RE = 12. Let V be the vector from point E to point R. Let J be the perpendicular bisector of segment RE. Point F is the translation of point R by vector V. Point A is the reflection of point E across point F. Point H is the reflection of point A across point E. Point W is on line J. Line K passes ... | 144.0 | MATH |
[
{
"content": "Let QR = 8. Let Y be the rotation of point Q by angle 5pi/12 around point R. Let B be the rotation of point R by angle 3pi/4 around point Y. Line M passes through points B and Y. Point O is the reflection of point R across point Q. Point J is obtained by rotating point R by angle pi/3 about point ... | 19.35 | MATH |
[
{
"content": "Let TJ = 7. Point L is obtained by rotating point J by angle 5pi/12 about point T. Point K is the reflection of point J across point T. Line U passes through point K perpendicular to segment LT. Line N is the reflection of line U across point J. Let D be the reflection of point T across point L. P... | 130.57 | MATH |
[
{
"content": "Let JP = 7. Let V be the rotation of point J by angle pi/6 around point P. Point A is the midpoint of segment PV. Line N is the angle bisector of angle VAJ. Let H be the line through point V parallel to line N. Point L is the reflection of point A across line H. Point O is the reflection of point ... | 9.91 | MATH |
[
{
"content": "Let ZN = 10. Point S is the reflection of point N across point Z. Point C is the midpoint of segment ZS. Line Y is the perpendicular bisector of segment CN. Point X is obtained by rotating point C by angle pi/2 about point N. Point M is obtained by rotating point S by angle 3pi/4 about point Z. Li... | 43.59 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.