messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let IB = 1. Let L be the vector from point B to point I. Let G be the rotation of point I by angle pi/3 around point B. Let Z be the midpoint of segment BG. Point M is the translation of point I by vector L. Line R passes through point M perpendicular to segment MZ. Point N is the midpoint of segm... | 0.96 | MATH |
[
{
"content": "YB = 12. Line T is the perpendicular bisector of segment YB. Line Q is the reflection of line T across point B. Point H is on line Q with |HB| = 3. Let L be the orthocenter of triangle YHB. Point O is the reflection of point L across segment YH. Point V is the reflection of point Y across line Q. ... | 77.67 | MATH |
[
{
"content": "ZQ = 5. Point D is obtained by rotating point Q by angle pi/6 about point Z. Point S is the incenter of triangle QDZ. Point V is the orthocenter of triangle QDZ. Point A is the reflection of point V across segment DZ. Find the length of segment SA. Express your answer as a decimal number rounded t... | 2.24 | MATH |
[
{
"content": "Let BG = 4. K is constructed so that GK = 6. Let P be the midpoint of segment KB. Let N be the midpoint of segment KP. Point A is the midpoint of segment PG. Find the length of segment AN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \... | 3.0 | MATH |
[
{
"content": "WK = 3. Let Q be the rotation of point W by angle 11pi/12 around point K. Let P be the reflection of point K across point Q. Point L is the midpoint of segment WP. Point E is the reflection of point K across point L. Point F is the reflection of point L across segment KW. What is the inradius of t... | 0.86 | MATH |
[
{
"content": "XY = 9. Let G be the rotation of point X by angle pi/2 around point Y. Let W be the line through point Y perpendicular to segment XY. Point R is on line W with |RY| = 8. Let Z be the midpoint of segment YG. Let J be the midpoint of segment XY. Point V is the reflection of point G across point J. P... | 18.0 | MATH |
[
{
"content": "Let RP = 7. Let C be the vector from point P to point R. Point I is obtained by rotating point R by angle 11pi/12 about point P. Let Y be point I translated by vector C. Let N be the midpoint of segment IY. Let X be the midpoint of segment RI. Point B is the incenter of triangle YRX. Find the circ... | 26.71 | MATH |
[
{
"content": "IF = 2. Point O is the reflection of point I across point F. Point A is obtained by rotating point I by angle pi/6 about point F. Let C be the midpoint of segment IF. Point J is the midpoint of segment CO. Let V be the reflection of point C across point A. Point L is the midpoint of segment JV. Wh... | 1.79 | MATH |
[
{
"content": "Let ZQ = 1. Let D be the rotation of point Q by angle pi/4 around point Z. Point E is the reflection of point Q across point Z. Point K is the midpoint of segment QZ. Let Y be the incircle of triangle KZD. Let O be the inversion of point Q in circle Y. Point J is the incenter of triangle KZD. What... | 0.01 | MATH |
[
{
"content": "TB = 1. Let U be the rotation of point B by angle pi/2 around point T. Point O is the incenter of triangle UTB. Let K be the line through points T and O. Point N is the intersection of segment BU and line K. Point M is the midpoint of segment BO. What is the length of segment MN? Express your answ... | 0.38 | MATH |
[
{
"content": "SY = 10. Let X be the rotation of point S by angle pi/2 around point Y. Let N be the midpoint of segment XY. Line A is the perpendicular bisector of segment NX. Let B be the reflection of point X across point S. Line J is the perpendicular bisector of segment SN. Point D is the reflection of point... | 0.47 | MATH |
[
{
"content": "Let EA = 11. Let T be the reflection of point A across point E. Let K be the rotation of point A by angle 11pi/12 around point E. Point D is the orthocenter of triangle EKA. Point P is the midpoint of segment TK. Point M is the reflection of point T across point A. Let R be the circumcenter of tri... | 2.61 | MATH |
[
{
"content": "Let QN = 6. Point C is the reflection of point Q across point N. Let K be the reflection of point N across point C. Line Z passes through points Q and C. Let S be the line through point C perpendicular to line Z. Let M be the rotation of point K by angle pi/2 around point N. Let V be the reflectio... | 53.85 | MATH |
[
{
"content": "HO = 7. Point S is the reflection of point H across point O. Let G be the midpoint of segment OH. Let U be the rotation of point G by angle pi/4 around point S. Point X is the reflection of point G across point U. Let M be the midpoint of segment OU. Point Y is the midpoint of segment XM. What is ... | 12.99 | MATH |
[
{
"content": "Let FI = 2. Let D be the rotation of point I by angle pi/4 around point F. Point O is the midpoint of segment FD. Let Y be the reflection of point O across point F. Point N is the midpoint of segment YF. Point E is the midpoint of segment IF. Point U is the reflection of point D across segment IN.... | 1.19 | MATH |
[
{
"content": "Let UH = 10. Let Z be the midpoint of segment UH. Point T is obtained by rotating point U by angle pi/6 about point Z. Point G is the reflection of point T across point H. Point J is the orthocenter of triangle ZUT. What is the inradius of triangle JHG? Express your answer as a decimal number roun... | 0.33 | MATH |
[
{
"content": "Let PZ = 12. Line X is the perpendicular bisector of segment ZP. Point L is the reflection of point Z across point P. Let O be the rotation of point P by angle pi/3 around point L. Point A is the reflection of point O across line X. Let N be the centroid of triangle LAO. Point T is the orthocenter... | 24.0 | MATH |
[
{
"content": "Let QR = 12. O is placed 12 units away from R. Let I be the rotation of point R by angle 5pi/6 around point O. Point M is the midpoint of segment OR. Let C be the midpoint of segment RQ. Let W be the reflection of point M across point C. Point E is the reflection of point R across segment WI. What... | 23.18 | MATH |
[
{
"content": "SJ = 5. Let P be the rotation of point S by angle 11pi/12 around point J. Let L be the perpendicular bisector of segment PJ. Point H is the reflection of point P across point S. Point G is the orthocenter of triangle HJP. Point N is the reflection of point H across line L. What is the length of se... | 118.99 | MATH |
[
{
"content": "HS = 6. Let X be the rotation of point H by angle pi/12 around point S. Let A be the midpoint of segment XH. Point P is obtained by rotating point X by angle pi/2 about point S. Let K be the reflection of point A across point H. Let O be the midpoint of segment PA. Let U be the reflection of point... | 5.27 | MATH |
[
{
"content": "Let NS = 10. O is constructed so that SO = 5. Let A be the centroid of triangle SON. Let M be the line through point A parallel to segment NS. Point J is the intersection of line M and segment ON. What is the distance between points J and A? Express your answer as a decimal number rounded to 2 dec... | 3.33 | MATH |
[
{
"content": "Let HY = 8. Let I be the midpoint of segment YH. Let A be the reflection of point I across point H. Let Z be the midpoint of segment YA. Line R is the perpendicular bisector of segment IH. Let M be the midpoint of segment YZ. Let V be the line through point M parallel to line R. Let C be the line ... | 11.69 | MATH |
[
{
"content": "JZ = 9. Let C be the reflection of point J across point Z. Let Y be the rotation of point Z by angle pi/12 around point C. Let F be the midpoint of segment JY. Let H be the incircle of triangle JYC. Let I be the incenter of triangle JYC. Point T is the inversion of point Y with respect to circle H... | 9.99 | MATH |
[
{
"content": "MK = 8. Point A is obtained by rotating point K by angle pi/4 about point M. Point N is the midpoint of segment MK. Point O is the reflection of point N across segment MA. Let Y be the midpoint of segment AK. What is the circumradius of triangle ONY? Express your answer as a decimal number rounded... | 3.46 | MATH |
[
{
"content": "Let BE = 3. Let L be the reflection of point E across point B. Let A be the rotation of point E by angle 11pi/12 around point L. Let Z be the midpoint of segment AB. Point K is the reflection of point B across point A. Point F is the reflection of point L across point E. What is the inradius of tr... | 0.39 | MATH |
[
{
"content": "IS = 8. Let R be the reflection of point S across point I. Line B passes through points R and S. Point L is obtained by rotating point S by angle pi/12 about point R. Point Q is the reflection of point L across line B. X is constructed so that RX = 3. Point V is the midpoint of segment IQ. Point J... | 5.76 | MATH |
[
{
"content": "Let PC = 8. Let W be the vector from point P to point C. Let I be the rotation of point P by angle 5pi/12 around point C. Point N is the translation of point I by vector W. Point D is the incenter of triangle NCI. Line U is the perpendicular bisector of segment IN. Line J is the reflection of line... | 8.64 | MATH |
[
{
"content": "CT = 4. Point S is obtained by rotating point T by angle pi/6 about point C. Point G is the reflection of point C across segment ST. Point E is the reflection of point G across point T. Point L is the reflection of point G across point E. What is the circumradius of triangle ELS? Express your answ... | 15.73 | MATH |
[
{
"content": "Let VC = 10. Point Q is obtained by rotating point V by angle pi/4 about point C. Point W is the reflection of point Q across point V. Point I is the midpoint of segment CQ. Let M be the midpoint of segment WC. Point G is the reflection of point M across segment CQ. Find the measure of angle IMG, ... | 20.71 | MATH |
[
{
"content": "NK = 10. Point E is obtained by rotating point K by angle pi/6 about point N. Let L be the centroid of triangle NEK. Let Q be the orthocenter of triangle NEK. Let C be the midpoint of segment QK. What is the length of segment CL? Express your answer as a decimal number rounded to 2 decimal places.... | 3.15 | MATH |
[
{
"content": "Let PB = 8. Let O be the rotation of point P by angle pi/4 around point B. Point S is the midpoint of segment BP. Point K is the midpoint of segment SP. Point G is the reflection of point K across point P. What is the circumradius of triangle KGO? Express your answer as a decimal number rounded to... | 3.57 | MATH |
[
{
"content": "Let MJ = 12. Let B be the midpoint of segment MJ. Let Q be the reflection of point B across point M. Line I is the perpendicular bisector of segment BJ. Let E be the reflection of point M across point Q. Let T be the rotation of point M by angle 2pi/3 around point E. Point W is the midpoint of seg... | 30.45 | MATH |
[
{
"content": "GU = 3. Line X is the perpendicular bisector of segment UG. Let Z be the reflection of line X through point U. Point B is the reflection of point U across point G. Let Y be the rotation of point U by angle pi/3 around point B. Let R be the midpoint of segment UG. Point P is the midpoint of segment... | 9.74 | MATH |
[
{
"content": "EH = 2. Point R is the midpoint of segment HE. Point T is the reflection of point R across point H. Let B be the reflection of point H across point T. Point L is obtained by rotating point B by angle 3pi/4 about point R. Let P be the rotation of point T by angle pi/6 around point E. Line D is the ... | 1.55 | MATH |
[
{
"content": "Let IE = 9. Let U be the reflection of point I across point E. Let T be the rotation of point U by angle 2pi/3 around point I. Point C is the midpoint of segment ET. Let W be the midpoint of segment TC. Let Q be the incenter of triangle ETU. Line G is the perpendicular bisector of segment IQ. Poin... | 3.74 | MATH |
[
{
"content": "Let DC = 9. Point G is obtained by rotating point D by angle 3pi/4 about point C. Let A be the perpendicular bisector of segment CG. Let J be the midpoint of segment DC. Line F passes through point D parallel to line A. Point T is the reflection of point J across line F. Find the distance between ... | 6.36 | MATH |
[
{
"content": "Let OC = 3. Point A is the reflection of point C across point O. Let N be the rotation of point C by angle 7pi/12 around point O. Line B is the perpendicular bisector of segment NO. Line V passes through point A parallel to line B. Point J is the reflection of point O across line V. Point U is the... | 0.97 | MATH |
[
{
"content": "MC = 2. Let E be the rotation of point C by angle 7pi/12 around point M. Point O is the centroid of triangle CME. Let V be the incenter of triangle CME. Circle A is the circumcircle of triangle CME. Let G be the inversion of point V in circle A. Let Y be the midpoint of segment OC. Let T be the in... | 0.73 | MATH |
[
{
"content": "Let SK = 7. Let N be the rotation of point S by angle pi/12 around point K. Point U is the reflection of point S across segment NK. Point T is the reflection of point N across point U. Let O be the midpoint of segment SN. Let Y be the reflection of point O across point K. What is the length of seg... | 13.68 | MATH |
[
{
"content": "Let VT = 6. Let X be the reflection of point V across point T. Point U is obtained by rotating point T by angle pi/4 about point V. Point G is the midpoint of segment UT. Let Z be the midpoint of segment UG. Let H be the orthocenter of triangle UXZ. Point C is the midpoint of segment ZH. What is t... | 5.37 | MATH |
[
{
"content": "Let WB = 11. Let X be the reflection of point W across point B. Let H be the rotation of point W by angle pi/12 around point X. Let D be the incenter of triangle HWX. Point P is the reflection of point B across segment HD. What is the distance between points P and X? Express your answer as a decim... | 20.78 | MATH |
[
{
"content": "DH = 1. Let O be the rotation of point H by angle 5pi/6 around point D. Point R is obtained by rotating point O by angle 5pi/12 about point D. Point V is the reflection of point R across point O. Point Y is the reflection of point V across segment DH. Let J be the perpendicular bisector of segment... | 1.66 | MATH |
[
{
"content": "CK = 1. Let I be the line through points K and C. Let Q be the line through point K perpendicular to line I. Point V is the reflection of point K across point C. Point G is on line Q with |GC| = 5. Point U is the reflection of point V across point G. Point M is the midpoint of segment GC. Let J be... | 8.01 | MATH |
[
{
"content": "Let DH = 11. Let T be the reflection of point D across point H. Point Y is obtained by rotating point D by angle 3pi/4 about point T. Let P be the reflection of point D across point Y. Let V be the line through points H and P. Point C is the reflection of point T across line V. Line K is the angle... | 1999.1 | MATH |
[
{
"content": "Let KQ = 2. Let L be the rotation of point K by angle 3pi/4 around point Q. Let F be the incenter of triangle LQK. Let O be the circumcenter of triangle LQK. Point H is the midpoint of segment KF. Line X passes through points O and H. Segment LQ and line X intersect at point Z. What is the distanc... | 1.04 | MATH |
[
{
"content": "Let BX = 9. Point R is obtained by rotating point X by angle 7pi/12 about point B. Let U be the perpendicular bisector of segment RX. Let W be the reflection of line U through point X. Let G be the line through points R and X. Point E is the midpoint of segment RB. Lines G and W intersect at point... | 10.59 | MATH |
[
{
"content": "DK = 1. Point O is the reflection of point D across point K. Let Y be the rotation of point D by angle 5pi/6 around point O. Line I is the perpendicular bisector of segment DY. Point L is the reflection of point K across line I. Point U is the reflection of point L across point D. What is the inra... | 0.15 | MATH |
[
{
"content": "Let DU = 12. Let J be the line through point D perpendicular to segment UD. Point Z is obtained by rotating point D by angle pi/4 about point U. Point Y is the midpoint of segment ZU. Let I be the rotation of point D by angle pi/6 around point U. Let G be the angle bisector of angle UYD. Point B i... | 7.29 | MATH |
[
{
"content": "Let PU = 2. Point S is obtained by rotating point P by angle pi/12 about point U. Point Z is the midpoint of segment SP. Let A be the line through point P perpendicular to segment US. Point M is the reflection of point Z across line A. Let R be the reflection of point Z across point M. Let Y be th... | 2.71 | MATH |
[
{
"content": "HR = 8. Point A is obtained by rotating point R by angle 5pi/12 about point H. Let B be the midpoint of segment RH. Point L is the reflection of point B across point R. Let J be the reflection of point L across point B. Find the distance between points J and B. Express your answer as a decimal num... | 8.0 | MATH |
[
{
"content": "ZJ = 9. Let X be the rotation of point Z by angle 2pi/3 around point J. Point V is obtained by rotating point J by angle 5pi/6 about point Z. Point C is the reflection of point X across segment ZJ. Let T be the reflection of point Z across point J. Let N be the midpoint of segment ZC. Find the cir... | 45.47 | MATH |
[
{
"content": "ME = 4. Point L is obtained by rotating point E by angle pi/2 about point M. Let A be the midpoint of segment LM. Let N be the line through points M and L. Point D is on line N with |DL| = 7. Point Z is the reflection of point D across segment ME. Let Y be the reflection of point L across point D.... | 0.5 | MATH |
[
{
"content": "Let DJ = 1. Point V is the reflection of point J across point D. Point Z is obtained by rotating point D by angle 3pi/4 about point J. Let Q be the midpoint of segment JZ. Let O be the reflection of point V across point Q. Let I be the incenter of triangle JZD. Find the length of segment IO. Expre... | 2.83 | MATH |
[
{
"content": "Let HS = 8. Point M is obtained by rotating point S by angle 3pi/4 about point H. Point E is the midpoint of segment SH. Point T is the reflection of point E across point S. Let R be the midpoint of segment ST. Let D be the line through point M parallel to segment HE. Point P is the reflection of ... | 3.52 | MATH |
[
{
"content": "JT = 1. Let V be the vector from point J to point T. Let K be the perpendicular bisector of segment TJ. Point E is the translation of point T by vector V. Let A be the line through point J parallel to line K. Line Y passes through point J perpendicular to line A. Let L be the line through point E ... | 1.5 | MATH |
[
{
"content": "EY = 2. Let M be the perpendicular bisector of segment YE. Point L lies on line M at distance 10 from point Y. Let S be the orthocenter of triangle YLE. Let I be the line through point E perpendicular to segment EY. Point Q is the reflection of point Y across line I. Find the length of segment QS.... | 3.0 | MATH |
[
{
"content": "KF = 8. Point D is obtained by rotating point K by angle pi/4 about point F. Point E is the midpoint of segment FK. Point S is the reflection of point E across point F. Point Q is the reflection of point S across segment KD. Point H is the midpoint of segment KD. Find the measure of angle EQH, in ... | 5.66 | MATH |
[
{
"content": "BD = 1. Point Q is obtained by rotating point B by angle 2pi/3 about point D. Let Y be the midpoint of segment BD. Point U is the centroid of triangle DQB. Point V is the midpoint of segment UB. Find the distance between points V and Y. Express your answer as a decimal number rounded to 2 decimal ... | 0.17 | MATH |
[
{
"content": "PL = 11. Let F be the rotation of point L by angle 7pi/12 around point P. Let Z be the rotation of point P by angle 2pi/3 around point L. Point C is obtained by rotating point F by angle 3pi/4 about point P. Point S is the reflection of point P across point Z. Point R is the reflection of point S ... | 52.39 | MATH |
[
{
"content": "Let QE = 9. Point P is obtained by rotating point E by angle 11pi/12 about point Q. Let N be the midpoint of segment QP. Let W be the centroid of triangle QEN. Let J be the midpoint of segment NW. What is the length of segment JW? Express your answer as a decimal number rounded to 2 decimal places... | 2.97 | MATH |
[
{
"content": "Let FI = 9. Let B be the rotation of point F by angle pi/6 around point I. Let R be the reflection of point I across point F. Point E is obtained by rotating point B by angle pi/2 about point F. Let X be the line through point E parallel to segment BR. Circle G is the incircle of triangle EBR. Let... | 13.54 | MATH |
[
{
"content": "Point T is the centroid of triangle B. Let U be the midpoint of segment BR. Let V be the reflection of point T across point U. Let J be the midpoint of segment VQ. What is the length of segment UJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex ... | 0.29 | MATH |
[
{
"content": "Let XM = 11. Let E be the rotation of point X by angle 5pi/12 around point M. Let T be the incenter of triangle XME. Point Y is the midpoint of segment XT. Point V is the midpoint of segment XY. Point U is the reflection of point V across segment XM. Find the distance between points U and Y. Expre... | 2.99 | MATH |
[
{
"content": "Let YZ = 6. Point Q is the reflection of point Z across point Y. Let N be the rotation of point Q by angle 3pi/4 around point Z. Point A is the reflection of point N across point Y. Let V be the midpoint of segment QA. Point F is the midpoint of segment YZ. Let S be the midpoint of segment VN. Let... | 9.55 | MATH |
[
{
"content": "Let ZT = 8. Let V be the reflection of point T across point Z. Point L is obtained by rotating point T by angle 7pi/12 about point V. Point N is the reflection of point T across point V. Let O be the rotation of point T by angle pi/6 around point L. Point I is the midpoint of segment VN. Let E be ... | 140.8 | MATH |
[
{
"content": "NF = 11. Let E be the rotation of point N by angle pi/4 around point F. Let R be the circumcircle of triangle EFN. Let Y be the incenter of triangle EFN. Let T be the inversion of point Y in circle R. Find the distance between points Y and T. Express your answer as a decimal number rounded to 2 de... | 23.98 | MATH |
[
{
"content": "RJ = 8. Point K is obtained by rotating point R by angle pi/12 about point J. Let O be the reflection of point J across point K. Let G be the rotation of point K by angle 11pi/12 around point O. Point T is the reflection of point O across point J. Circle Q is the incircle of triangle RGJ. Let I be... | 0.01 | MATH |
[
{
"content": "Let ZI = 11. Let K be the rotation of point Z by angle 7pi/12 around point I. Let S be the midpoint of segment ZK. Point F is the reflection of point I across segment SZ. Point U is the incenter of triangle ISZ. Find the length of segment UF. Express your answer as a decimal number rounded to 2 de... | 9.18 | MATH |
[
{
"content": "IZ = 2. Point P is obtained by rotating point Z by angle 5pi/6 about point I. Point K is the reflection of point P across point Z. Point B is the centroid of triangle ZIP. Point O is the midpoint of segment IB. What is the inradius of triangle OKI? Express your answer as a decimal number rounded t... | 0.08 | MATH |
[
{
"content": "Let BQ = 2. Point T is the midpoint of segment QB. Let A be the vector from point T to point B. Let E be the midpoint of segment BT. Let Z be point B translated by vector A. Let L be the line through point Z perpendicular to segment QB. Let D be the line through point T perpendicular to segment QB... | 57.5 | MATH |
[
{
"content": "ID = 5. Point R is obtained by rotating point D by angle 2pi/3 about point I. Point L is the midpoint of segment IR. Let H be the angle bisector of angle ILR. Point A lies on line H at distance 8 from point I. Point S is the midpoint of segment RA. Let E be the reflection of point S across point A... | 5.4 | MATH |
[
{
"content": "Let OK = 4. Let Q be the midpoint of segment KO. Point F is obtained by rotating point O by angle 11pi/12 about point K. Let L be the reflection of point F across point O. Point X is obtained by rotating point F by angle pi/6 about point O. Let A be the reflection of point O across point X. Let R ... | 4.94 | MATH |
[
{
"content": "OW = 9. Point R is obtained by rotating point W by angle 5pi/6 about point O. Point D is the midpoint of segment OW. Let G be the midpoint of segment DW. Point L is the reflection of point G across segment RD. What is the circumradius of triangle LRW? Express your answer as a decimal number rounde... | 11.25 | MATH |
[
{
"content": "Let NH = 4. Let K be the rotation of point N by angle 2pi/3 around point H. Point M is the midpoint of segment KN. Let I be the centroid of triangle MHN. Let O be the incenter of triangle MHN. What is the distance between points I and O? Express your answer as a decimal number rounded to 2 decimal... | 0.43 | MATH |
[
{
"content": "FT = 3. Let N be the rotation of point T by angle 3pi/4 around point F. Let V be the rotation of point N by angle pi/6 around point T. Let Z be the angle bisector of angle VFT. Point J is the reflection of point F across point N. Point O is the reflection of point T across line Z. Point P is the i... | 0.06 | MATH |
[
{
"content": "PF = 9. Point B is the reflection of point F across point P. Point Q is the reflection of point P across point B. Point U is obtained by rotating point F by angle pi/3 about point B. Line C is the angle bisector of angle BUQ. Let K be the midpoint of segment BU. Let R be the reflection of line C t... | 61.45 | MATH |
[
{
"content": "KB = 10. Point P is the midpoint of segment KB. Line H is the angle bisector of angle BKP. Let V be the reflection of point K across point B. Point Z is on line H with |ZP| = 9. Point G is obtained by rotating point Z by angle 7pi/12 about point P. Let F be the perpendicular bisector of segment PV... | 16.3 | MATH |
[
{
"content": "GI = 5. Point Y is obtained by rotating point I by angle pi/3 about point G. Let R be the rotation of point Y by angle pi/4 around point I. Line B passes through point G perpendicular to segment IR. Let F be the midpoint of segment RY. Point C is the reflection of point F across line B. Find the m... | 1.72 | MATH |
[
{
"content": "RY = 11. Point V is the midpoint of segment RY. Let X be the rotation of point R by angle pi/2 around point Y. Point O is the centroid of triangle VXY. Let G be the perpendicular bisector of segment VX. Line L is the reflection of line G across point R. Point K is the reflection of point O across ... | 32.24 | MATH |
[
{
"content": "Let IF = 9. Let R be the rotation of point I by angle 5pi/6 around point F. Let H be the reflection of point R across point I. Let C be the circumcenter of triangle FIH. Let E be the midpoint of segment FI. Point U is the reflection of point C across point R. Find the distance between points E and... | 33.38 | MATH |
[
{
"content": "Let LA = 7. Point K is the midpoint of segment LA. Point E is obtained by rotating point K by angle pi/2 about point L. Point I is the midpoint of segment KL. Point D is the centroid of triangle LIE. Let T be the midpoint of segment EL. Let B be the reflection of point T across point D. Point C is... | 1.2 | MATH |
[
{
"content": "GV = 9. Point D is obtained by rotating point G by angle 7pi/12 about point V. Point E is the reflection of point V across point D. Point N is obtained by rotating point D by angle 11pi/12 about point E. Point K is the orthocenter of triangle NED. Circle S is the circumcircle of triangle NED. Let ... | 27.01 | MATH |
[
{
"content": "Let UY = 7. Let N be the midpoint of segment YU. Point P is obtained by rotating point N by angle 7pi/12 about point U. Circle M is the incircle of triangle NUP. Let J be the reflection of circle M through point Y. Let V be the rotation of point Y by angle 5pi/6 around point U. Let C be the midpoi... | 3.19 | MATH |
[
{
"content": "OC = 9. Point P is obtained by rotating point O by angle 3pi/4 about point C. Point K is obtained by rotating point P by angle 11pi/12 about point O. Let W be the midpoint of segment CK. Let F be the centroid of triangle WOP. Point L is the reflection of point F across segment OP. Find the measure... | 10.49 | MATH |
[
{
"content": "MG = 10. Point P is the reflection of point G across point M. Let K be the rotation of point M by angle pi/6 around point G. Point I is the reflection of point G across segment PK. Line V passes through point P perpendicular to segment PK. Let O be the line through point I parallel to line V. Poin... | 80.67 | MATH |
[
{
"content": "KF = 3. Line E is the perpendicular bisector of segment KF. Point A lies on line E at distance 6 from point K. Point L is the incenter of triangle KFA. Point B is the orthocenter of triangle KFA. Line I passes through point L parallel to segment KF. Segment FA and line I intersect at point W. Find... | 1.45 | MATH |
[
{
"content": "YK = 6. Point U is obtained by rotating point K by angle 2pi/3 about point Y. Point A is obtained by rotating point K by angle 11pi/12 about point U. Point J is the reflection of point A across point U. Let Q be the centroid of triangle KYJ. Let Z be the line through point U perpendicular to segme... | 0.77 | MATH |
[
{
"content": "Let FA = 6. Let U be the rotation of point A by angle pi/12 around point F. Let P be the rotation of point F by angle 2pi/3 around point A. Let G be the reflection of point A across point P. Point K is the midpoint of segment PG. Let Q be the midpoint of segment KF. Point Z is the reflection of po... | 23.52 | MATH |
[
{
"content": "ZC = 4. Let J be the midpoint of segment ZC. Point L is obtained by rotating point Z by angle 7pi/12 about point J. Point R is obtained by rotating point J by angle 3pi/4 about point C. Let Y be the perpendicular bisector of segment JL. Point Q is the reflection of point Z across line Y. Point P i... | 0.92 | MATH |
[
{
"content": "Let US = 10. Point V is obtained by rotating point U by angle pi/12 about point S. Point O is the reflection of point U across point S. Let B be the midpoint of segment SO. Let N be the centroid of triangle OVU. Point J is the reflection of point N across segment VU. Find the distance between poin... | 21.48 | MATH |
[
{
"content": "Let GT = 12. Let A be the rotation of point T by angle pi/4 around point G. Point O is the orthocenter of triangle GTA. Let V be the incenter of triangle GTA. Let F be the midpoint of segment TA. Point C is the midpoint of segment VF. Point R is the midpoint of segment CT. Point L is on segment TA... | 1.17 | MATH |
[
{
"content": "NZ = 3. Let L be the midpoint of segment NZ. Line E is the perpendicular bisector of segment ZN. Line X passes through point N parallel to line E. Let M be the reflection of line X across line E. Point D lies on line M at distance 5 from point N. Point P lies on line X. Let T be the reflection of ... | 2.5 | MATH |
[
{
"content": "Let IM = 11. Let H be the midpoint of segment IM. Point P is obtained by rotating point H by angle 11pi/12 about point I. Let O be the reflection of point P across point M. Point V is the orthocenter of triangle IOP. Point R is the reflection of point O across segment VP. What is the distance betw... | 32.75 | MATH |
[
{
"content": "YG = 4. Let N be the vector from point G to point Y. Point U is the translation of point Y by vector N. Let T be the reflection of point G across point U. Let V be the rotation of point T by angle 5pi/12 around point Y. Let B be the rotation of point U by angle pi/12 around point V. Line X is the ... | 30.62 | MATH |
[
{
"content": "Let GZ = 10. Point X is obtained by rotating point Z by angle pi/12 about point G. Point Q is the midpoint of segment GX. Let M be the reflection of point Q across point Z. Circle R is the circumcircle of triangle GXZ. Point C is the incenter of triangle GXZ. Point D is the reflection of point M a... | 2.03 | MATH |
[
{
"content": "Let QG = 11. Let B be the rotation of point G by angle 7pi/12 around point Q. Let H be the midpoint of segment GQ. Line E passes through point H perpendicular to segment GQ. Let R be the midpoint of segment HB. Point W is the reflection of point B across line E. What is the inradius of triangle GR... | 3.31 | MATH |
[
{
"content": "DM = 3. Let U be the reflection of point D across point M. Point C is the reflection of point M across point U. Point N is obtained by rotating point C by angle pi/4 about point U. Let Y be the reflection of point N across point C. Point A is the reflection of point N across point U. Point R is th... | 6.49 | MATH |
[
{
"content": "XY = 12. Let A be the rotation of point Y by angle pi/4 around point X. Let U be the midpoint of segment YA. Let L be the incenter of triangle XYA. Point S is the midpoint of segment XY. Find the measure of angle LUS, in radians. Express your answer as a decimal number rounded to 2 decimal places.... | 3.52 | MATH |
[
{
"content": "YA = 4. Let D be the rotation of point Y by angle pi around point A. Point X is the midpoint of segment AD. Let H be the rotation of point A by angle pi/4 around point Y. Point Z is the reflection of point H across point A. Point B is the reflection of point H across point D. Let T be the orthocen... | 5.97 | MATH |
[
{
"content": "Let RX = 8. Let M be the rotation of point X by angle pi/6 around point R. Let E be the reflection of point R across point X. Point N is the reflection of point M across segment RX. Point B is the reflection of point N across point M. Let C be the reflection of point R across point B. Find the cir... | 12.09 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.