[User]
HB = 11. Point Q is the reflection of point B across point H. Let L be the midpoint of segment BH. Point T is obtained by rotating point H by angle 2pi/3 about point Q. Let E be the line through points T and Q. Line V is the perpendicular bisector of segment BH. Line I is the reflection of line E across line V. Line O is the reflection of line E across line I. Point K is the reflection of point H across line O. What is the length of segment KL? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
FU = 5. Point W is the reflection of point F across point U. Point H is obtained by rotating point W by angle pi/4 about point U. Let J be the midpoint of segment WH. Point Q is the reflection of point H across segment UF. Line Y is the perpendicular bisector of segment UF. Let O be the reflection of point H across point W. Point C is the midpoint of segment QH. Let A be the rotation of point U by angle 11pi/12 around point J. Let L be the midpoint of segment JC. Line N is the reflection of line Y across point A. Line G passes through point L parallel to segment UF. Point B is the intersection of lines N and G. What is the distance between points O and B? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let JY = 9. Let V be the perpendicular bisector of segment YJ. Let D be the midpoint of segment YJ. Let Z be the reflection of point Y across point J. Point U is on line V with |UJ| = 12. Line P is the perpendicular bisector of segment YZ. Let H be the line through point Z parallel to line P. Point G is the midpoint of segment DU. Point C is the reflection of point G across line H. Point O is the reflection of point Z across point U. Find the length of segment CO. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
IP = 6. Let Q be the midpoint of segment IP. Let D be the reflection of point I across point P. Point M is the reflection of point Q across point D. Let X be the midpoint of segment QI. Find the length of segment MX. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let PM = 6. Let U be the rotation of point P by angle pi/2 around point M. Let T be the angle bisector of angle UMP. Let Q be the midpoint of segment UP. Let B be the midpoint of segment MU. Let I be the line through point B perpendicular to line T. Point L is the reflection of point U across line I. What is the distance between points L and Q? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
JO = 2. Let K be the rotation of point O by angle pi/4 around point J. Let V be the line through points J and O. Point Q is the midpoint of segment OJ. Line M is the angle bisector of angle JKQ. Let Z be the reflection of line V across line M. Point A is the reflection of point K across line Z. Point U is the reflection of point O across segment QA. Point H is the intersection of line Z and segment QA. Point N is the reflection of point U across point H. What is the length of segment QN? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
MS = 8. Let K be the rotation of point S by angle 5pi/6 around point M. Let N be the rotation of point K by angle pi/3 around point M. Let W be the midpoint of segment SN. Point B is obtained by rotating point W by angle pi about point K. Point U is the reflection of point M across point N. Line X passes through points B and S. Line J passes through points W and U. Line L is the angle bisector of angle WNB. Let O be the line through point U parallel to line L. Line F is the reflection of line X across line J. Point Z is the intersection of lines X and O. Point A is the reflection of point K across line O. Let T be the midpoint of segment SZ. Let E be the line through point K parallel to line F. Point D is the reflection of point A across line F. Point I is the reflection of point D across segment MT. Point G is the midpoint of segment BI. Point V is the intersection of segment BN and line E. What is the distance between points V and G? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
WD = 12. Let N be the reflection of point W across point D. Let V be the midpoint of segment DN. Point F is obtained by rotating point N by angle 7pi/12 about point W. Line Z passes through points F and W. Point R is the reflection of point D across line Z. Point J is the midpoint of segment VD. Let K be the reflection of point F across point J. Find the distance between points K and R. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
SL = 5. Point N is obtained by rotating point L by angle 7pi/12 about point S. Let T be the rotation of point S by angle pi/4 around point N. Point H is the midpoint of segment NL. Let C be the reflection of point H across point N. Let U be the line through point C parallel to segment NT. Point M is the reflection of point N across line U. What is the distance between points M and C? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
AY = 1. Let N be the perpendicular bisector of segment YA. Let H be the reflection of line N through point Y. Let U be the rotation of point A by angle 7pi/12 around point Y. Point Q is the reflection of point Y across line H. Let L be the midpoint of segment YQ. Point M is the midpoint of segment YL. Point G is obtained by rotating point Q by angle 7pi/12 about point U. Let J be the perpendicular bisector of segment GM. Let O be the reflection of line J through point Y. Point I is the midpoint of segment GU. Point R is the reflection of point L across line O. Find the distance between points R and I. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
BN = 4. Let J be the line through points B and N. Point Y is obtained by rotating point B by angle 7pi/12 about point N. Point A is the midpoint of segment NB. Let X be the rotation of point A by angle 11pi/12 around point Y. Point K is the midpoint of segment AX. Point D is the reflection of point K across line J. Line V is the perpendicular bisector of segment KA. Point M is the reflection of point D across line V. Find the length of segment MY. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let TC = 5. Let H be the midpoint of segment TC. Let TN = 1. Line I is the angle bisector of angle HTN. Let O be the reflection of line I through point H. Point W is on segment NT. Line X passes through point W perpendicular to segment NT. Line J is the reflection of line X across line I. Line S is the reflection of line J across line O. Point Q is the midpoint of segment NT. Point D lies on line S. Let Z be the midpoint of segment DQ. Let A be the midpoint of segment TD. What is the length of segment ZA? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let HR = 1. Let Q be the reflection of point H across point R. Let W be the rotation of point Q by angle pi/12 around point R. Let Z be the rotation of point W by angle pi around point Q. Line T is the perpendicular bisector of segment ZQ. Line K passes through point H parallel to line T. Let X be the angle bisector of angle ZHW. Let U be the rotation of point Q by angle 5pi/6 around point R. Point V is the reflection of point U across line X. Let F be the reflection of line X through point R. Point P is the intersection of lines F and K. Let S be the midpoint of segment HP. What is the length of segment VS? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
KM = 4. Let Y be the midpoint of segment KM. Line Z is the perpendicular bisector of segment YM. Point E is the reflection of point K across line Z. Let F be the rotation of point K by angle 3pi/4 around point E. Line H is the angle bisector of angle FMK. Point Q is the reflection of point Y across line H. Line C is the perpendicular bisector of segment QF. Point P is the reflection of point M across line C. Find the length of segment PY. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let HR = 11. Let S be the reflection of point H across point R. Let V be the rotation of point H by angle 3pi/4 around point R. Let J be the rotation of point R by angle pi/2 around point V. Let U be the reflection of point S across point J. Point W is obtained by rotating point S by angle 2pi/3 about point J. Let K be the rotation of point H by angle pi/4 around point U. Line G is the angle bisector of angle HVW. Point F is the midpoint of segment WK. Line Y is the reflection of line G across point F. Line Z passes through point V perpendicular to line G. Let I be the reflection of line Z through point S. Point D is the intersection of lines I and Y. Find the distance between points K and D. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
DA = 3. Let O be the midpoint of segment DA. Point M is the midpoint of segment AO. Let L be the midpoint of segment MO. Let Q be the midpoint of segment LD. Let W be the reflection of point D across point L. Let G be the midpoint of segment DQ. Line T is the perpendicular bisector of segment LD. Line P passes through point O perpendicular to segment LD. Point I is the midpoint of segment QG. Line Z passes through point W parallel to line T. Let E be the line through point M parallel to line Z. Point F is the reflection of point W across line P. Point N is the reflection of point F across line E. Let Y be the midpoint of segment NL. Find the distance between points I and Y. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let RQ = 5. Point G is obtained by rotating point Q by angle pi/2 about point R. Point W is the reflection of point G across point R. Let O be the rotation of point G by angle 7pi/12 around point Q. Point J is the reflection of point W across point O. Point Z is the midpoint of segment OJ. Line S is the perpendicular bisector of segment OJ. Line H is the angle bisector of angle JZG. Line B is the reflection of line H across line S. Point X is the intersection of segment RJ and line B. Find the distance between points W and X. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
ME = 10. Let T be the rotation of point E by angle pi/12 around point M. Point Y is the midpoint of segment ET. Line J is the perpendicular bisector of segment YT. Line Q is the reflection of line J across point Y. Point S is the reflection of point M across line Q. What is the distance between points S and M? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
QK = 11. Point Y is the midpoint of segment KQ. Point A is the reflection of point Q across point K. Let W be the rotation of point K by angle pi/4 around point Y. Point V is the midpoint of segment YA. Point P is the midpoint of segment WA. Point N is the reflection of point Y across point Q. Point D is the reflection of point V across point N. What is the distance between points P and D? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
YB = 2. Let H be the midpoint of segment BY. Let W be the perpendicular bisector of segment YB. Line Q is the reflection of line W across point B. Let S be the reflection of point H across point B. Let U be the line through point B perpendicular to line Q. Point F is obtained by rotating point S by angle pi/12 about point B. Let G be the reflection of point Y across point F. Let E be the reflection of line U through point G. Line O is the reflection of line E across line U. Point T is the reflection of point S across point H. Point C is the reflection of point H across line O. Find the length of segment TC. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
VO = 6. Let X be the vector from point O to point V. Point B is the translation of point V by vector X. Point Q is obtained by rotating point V by angle 3pi/4 about point O. Let R be the rotation of point O by angle pi/3 around point Q. Let M be the angle bisector of angle QRO. Line S passes through points O and B. Point T is the reflection of point R across point O. Point L is the midpoint of segment VB. Line K is the reflection of line M across line S. Point U is obtained by rotating point T by angle pi/2 about point V. Let D be the rotation of point Q by angle 2pi/3 around point U. Let W be the line through points L and D. Let H be the midpoint of segment VT. Point G is the midpoint of segment HV. Point P is the intersection of lines W and K. Find the length of segment GP. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
JW = 1. Point F is obtained by rotating point J by angle pi/3 about point W. Line Y passes through points W and F. Point I is the reflection of point J across line Y. Point B is the reflection of point J across point F. Let Z be the midpoint of segment BI. What is the length of segment ZB? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
UM = 4. Let D be the rotation of point M by angle pi/3 around point U. Line S passes through points M and D. Let L be the midpoint of segment UD. Let C be the midpoint of segment LM. Let E be the midpoint of segment LD. Point V is the reflection of point C across line S. Point J is the midpoint of segment DM. Point Q is the reflection of point J across segment CE. Let I be the rotation of point L by angle 11pi/12 around point V. Point B is obtained by rotating point E by angle 5pi/12 about point V. Let H be the angle bisector of angle JQI. Point F is the reflection of point B across line H. Point Z is the reflection of point J across segment LD. Let Y be the midpoint of segment ZU. What is the distance between points F and Y? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let XN = 4. Let R be the vector from point N to point X. Let O be the rotation of point X by angle 7pi/12 around point N. Point E is the translation of point X by vector R. Let S be the reflection of point X across point E. Point J is obtained by rotating point O by angle pi/3 about point E. Let B be the midpoint of segment XE. Let V be the reflection of point J across point E. Let C be the perpendicular bisector of segment SO. Let Y be the reflection of line C through point V. Point H is the reflection of point X across line Y. Point D is the midpoint of segment OE. Point U is the reflection of point E across line C. Let Z be the reflection of point D across point B. Point A is the midpoint of segment JX. Point T is the reflection of point A across segment HE. Let L be the midpoint of segment ZU. Find the length of segment LT. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
PI = 1. Point V is obtained by rotating point I by angle pi/12 about point P. Let A be the midpoint of segment PV. Let F be the angle bisector of angle IAP. Point T is the reflection of point V across point P. Point C is the midpoint of segment PI. Let X be the line through point P parallel to line F. Let M be the perpendicular bisector of segment CV. Point N is the midpoint of segment PA. Let O be the line through point N parallel to line M. Lines O and X intersect at point S. Point R is the midpoint of segment SV. What is the length of segment TR? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
QJ = 5. Point M is obtained by rotating point J by angle 11pi/12 about point Q. Let H be the reflection of point M across point Q. Point N is the midpoint of segment QH. Point P is the reflection of point N across segment JQ. Find the length of segment PH. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let UC = 11. Let T be the rotation of point U by angle 11pi/12 around point C. Let G be the rotation of point U by angle pi/3 around point T. Point V is the midpoint of segment TG. Point F is the midpoint of segment UV. Let L be the midpoint of segment FU. Line Q is the angle bisector of angle VGC. Line Y passes through point V perpendicular to line Q. Let N be the perpendicular bisector of segment LF. Let A be the perpendicular bisector of segment UF. Let M be the reflection of point T across point G. Line B is the reflection of line Y across line N. Line B and segment TG intersect at point J. Point Z is the reflection of point J across point M. Point E is the reflection of point M across line A. What is the length of segment EZ? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
ID = 3. Let G be the reflection of point I across point D. Line P is the angle bisector of angle GDI. Line Z passes through point D perpendicular to line P. Point Y lies on line P at distance 5 from point D. Let B be the rotation of point D by angle pi/12 around point Y. Line K is the reflection of line Z across point B. Point M is the reflection of point G across line K. Point L is the midpoint of segment GM. What is the length of segment LI? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let AW = 10. Let D be the line through points A and W. Point F is the reflection of point W across point A. Let K be the vector from point W to point A. Line N passes through point W perpendicular to line D. Let M be the midpoint of segment FA. Point P is the translation of point M by vector K. Point B is obtained by rotating point F by angle 11pi/12 about point W. Point Q is the reflection of point P across line N. Let Y be the midpoint of segment MW. Point X is the reflection of point Q across segment MB. Find the length of segment YX. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let YX = 4. Let YL = 2. Let V be the perpendicular bisector of segment LY. Point Z is the reflection of point L across point X. Point E is on line V with |EZ| = 2. Point M is obtained by rotating point E by angle pi/2 about point X. Let G be the midpoint of segment MX. Point N is the reflection of point L across point Y. Point A is the reflection of point L across segment MG. Point H is the reflection of point N across segment MG. What is the distance between points A and H? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let KA = 11. Line O passes through points K and A. Point Y is the reflection of point A across point K. Point G is obtained by rotating point A by angle pi/3 about point Y. Line V passes through point G parallel to line O. Point H is the reflection of point K across point A. Point F is the reflection of point K across line V. Let M be the reflection of line O through point F. Point N is the reflection of point F across point A. Point X is the midpoint of segment FH. Point U is the reflection of point X across line M. What is the distance between points U and N? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
DK = 8. Let S be the reflection of point K across point D. Let Q be the reflection of point D across point K. Let L be the rotation of point Q by angle 11pi/12 around point K. Line B is the perpendicular bisector of segment LD. Line T passes through point L parallel to line B. Let Y be the midpoint of segment LD. Point C is the reflection of point S across line T. Point G is the midpoint of segment YC. Find the distance between points Y and G. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
DI = 12. Point T is obtained by rotating point I by angle 7pi/12 about point D. Let F be the vector from point D to point T. Let Y be the midpoint of segment ID. Let X be the line through point I parallel to segment YT. Let C be the reflection of line X through point T. Line P passes through points T and D. Let J be point I translated by vector F. Point S is the reflection of point J across line P. Line N is the angle bisector of angle SJD. Let E be the line through point T parallel to line N. Let K be the reflection of line E across line C. Point M is the intersection of lines X and K. Find the distance between points M and J. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let GN = 2. Let T be the reflection of point G across point N. Point Y is the reflection of point N across point T. Point U is obtained by rotating point T by angle pi/3 about point G. Let A be the angle bisector of angle UNT. Line E is the perpendicular bisector of segment NU. Line P is the angle bisector of angle GYU. Line O passes through point U parallel to line E. Let C be the line through point G perpendicular to line P. Line S is the reflection of line C across line A. Point X is the reflection of point N across line C. Point H is the reflection of point U across point N. Point L is the reflection of point X across line S. Point D is the reflection of point H across line O. Point I is the reflection of point T across point L. What is the distance between points D and I? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
CO = 9. Point S is the midpoint of segment CO. Let M be the rotation of point S by angle 2pi/3 around point C. Point H is the midpoint of segment OS. Let T be the vector from point C to point H. Point W is the translation of point H by vector T. Let L be point M translated by vector T. Point V is obtained by rotating point M by angle 5pi/12 about point L. Point B is the midpoint of segment WV. Let U be the midpoint of segment BC. Point Z is the midpoint of segment VU. What is the distance between points Z and W? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
EM = 12. Point D is the midpoint of segment ME. Line C is the perpendicular bisector of segment ME. Point J is on line C with |JD| = 6. Point S is the reflection of point J across segment ME. Let G be the midpoint of segment ED. Point A is the midpoint of segment SE. What is the measure of angle EAG, in radians? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
XR = 6. Point F is obtained by rotating point X by angle 5pi/12 about point R. Point U is obtained by rotating point F by angle pi/12 about point R. Point L is the midpoint of segment RU. Point K is the reflection of point L across segment UF. Let T be the midpoint of segment XK. What is the length of segment FT? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
JZ = 9. Let T be the reflection of point J across point Z. Let K be the perpendicular bisector of segment JT. Point A is the midpoint of segment ZJ. Point Y is obtained by rotating point A by angle pi/2 about point T. Let E be the perpendicular bisector of segment JA. Let M be the reflection of line K across line E. Let V be the line through point Y parallel to segment ZJ. Let R be the reflection of line E across line M. Point S is the intersection of lines R and V. What is the distance between points S and T? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
AM = 12. Point P is the reflection of point A across point M. Point I is obtained by rotating point P by angle pi/4 about point M. Let G be the perpendicular bisector of segment PM. Let F be the line through point P perpendicular to line G. Let T be the rotation of point I by angle pi/12 around point A. Point H is the midpoint of segment MI. Point L is the reflection of point H across line F. Let K be the reflection of point L across point T. Point C is the reflection of point K across segment MT. Find the distance between points H and C. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
RB = 2. Let X be the vector from point R to point B. Let E be the rotation of point B by angle pi/3 around point R. Point T is the reflection of point E across point R. Let Q be the line through points B and T. Point A is the translation of point T by vector X. Let P be the rotation of point T by angle pi/12 around point R. Line D is the reflection of line Q across point A. Point C is the reflection of point E across line D. Point M is the midpoint of segment CB. Point Z is the midpoint of segment PC. What is the distance between points Z and M? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let AS = 8. Let L be the reflection of point A across point S. Let Z be the vector from point A to point L. Point C is the midpoint of segment LS. Point X is obtained by rotating point A by angle 11pi/12 about point L. Let B be the perpendicular bisector of segment LX. Let D be the rotation of point S by angle pi/3 around point C. Point J is the reflection of point D across segment SL. Let P be the reflection of point A across point L. Point R is the translation of point P by vector Z. Point U is the translation of point R by vector Z. Let T be the midpoint of segment JL. Let H be point U translated by vector Z. Let G be the midpoint of segment DH. Point O is the reflection of point G across line B. Let I be the midpoint of segment AT. Point N is the midpoint of segment OC. What is the distance between points I and N? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
NF = 9. S is placed 6 units away from F. Let NW = 1. Point B is the midpoint of segment SF. Point M is the reflection of point B across segment WS. Point K is the reflection of point F across segment WS. Find the distance between points M and K. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let VC = 1. Let Z be the vector from point V to point C. Point R is obtained by rotating point V by angle 5pi/12 about point C. Let Y be the vector from point R to point C. Point G is obtained by rotating point C by angle pi/12 about point R. Point D is the translation of point G by vector Y. Point W is the reflection of point V across segment GR. Point X is the intersection of segments VC and GR. Let P be point D translated by vector Z. Point A is the reflection of point P across segment VC. Point J is the reflection of point C across segment GR. Line O is the perpendicular bisector of segment PW. Let K be the reflection of line O through point X. Let L be the midpoint of segment RJ. Point S is the midpoint of segment LD. Point T is the reflection of point A across line K. Find the distance between points T and S. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
FS = 9. Point L is obtained by rotating point F by angle 5pi/6 about point S. Point T is the reflection of point F across point L. Let K be the reflection of point L across point S. Let O be the reflection of point K across point T. Point I is the midpoint of segment SL. Let G be the midpoint of segment TI. Let X be the midpoint of segment TG. Let P be the midpoint of segment FO. Point J is the midpoint of segment PX. What is the length of segment PJ? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
EW = 3. Let Q be the perpendicular bisector of segment EW. Let B be the rotation of point E by angle pi/4 around point W. Point G is the midpoint of segment BW. Point D is the midpoint of segment EB. Let H be the line through point E perpendicular to line Q. Let A be the midpoint of segment ED. Let X be the line through point W parallel to line Q. Let R be the reflection of point B across point A. Let U be the rotation of point R by angle 11pi/12 around point E. Let F be the line through point D perpendicular to line H. Let I be the line through points B and A. Line Z passes through points D and G. Line M is the reflection of line I across line X. Let L be the reflection of line X across line F. Point P is the reflection of point U across line L. Lines Z and M intersect at point J. What is the distance between points J and P? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
FM = 9. Point D is obtained by rotating point F by angle 2pi/3 about point M. Point E is obtained by rotating point F by angle pi/4 about point M. Let K be the rotation of point D by angle 5pi/6 around point F. Let I be the vector from point D to point F. Let O be point M translated by vector I. Line V is the angle bisector of angle EOF. Point B is the reflection of point F across line V. Let A be the line through points F and M. Line Q passes through point O perpendicular to line A. Line G passes through points B and F. Let R be point B translated by vector I. Let C be the midpoint of segment FK. Let H be the reflection of line Q across line G. Point W is the reflection of point R across segment FK. Let U be the midpoint of segment WR. Point J is the intersection of lines A and H. Point P is the midpoint of segment JC. What is the length of segment UP? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let JF = 6. Point Q is the reflection of point F across point J. Let P be the angle bisector of angle FQJ. Let W be the line through point F perpendicular to line P. JC = 9. Line L is the perpendicular bisector of segment QJ. Point Y lies on line L at distance 12 from point Q. Point N is the reflection of point J across line W. Let T be the midpoint of segment YJ. Point D lies on segment CN. Point A is the reflection of point T across line W. Point I is the midpoint of segment DT. Point G is the reflection of point A across point I. Find the length of segment DG. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
WR = 2. Point H is the reflection of point R across point W. Let X be the midpoint of segment RW. Let F be the perpendicular bisector of segment HX. Point K is the reflection of point X across point H. Point D is the reflection of point H across point K. Point T is the reflection of point K across line F. Point O is the midpoint of segment DW. Point G is on line F with |GT| = 2. Point V is obtained by rotating point D by angle pi about point G. Line M is the perpendicular bisector of segment VG. Let N be the midpoint of segment VR. Line S is the reflection of line M across point O. Point B is the reflection of point K across point N. Point U is the reflection of point B across line S. Let L be the reflection of point O across point G. What is the length of segment UL? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let SC = 6. Let I be the rotation of point S by angle pi/6 around point C. Let O be the line through point C perpendicular to segment CS. Point F is the reflection of point I across line O. Point B is the midpoint of segment CS. Point N is the midpoint of segment BI. Let G be the midpoint of segment NF. Let L be the midpoint of segment FI. What is the distance between points L and G? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let OM = 9. Point E is the reflection of point M across point O. Line B passes through points O and E. Point I is the reflection of point O across point M. Let D be the rotation of point I by angle 5pi/12 around point O. Let Q be the midpoint of segment MD. Let J be the midpoint of segment IQ. Point U is the reflection of point J across line B. Let G be the reflection of point M across point U. Find the length of segment QG. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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RV = 1. Point F is the midpoint of segment VR. Point K is the reflection of point F across point V. Let H be the rotation of point K by angle 5pi/6 around point V. Point W is the reflection of point R across segment KH. Point Y is the reflection of point R across segment HW. Point Q is the reflection of point V across segment KH. What is the length of segment YQ? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let MB = 7. Line T passes through points M and B. Point P is the midpoint of segment BM. Let Z be the reflection of point P across point M. Line X passes through point Z perpendicular to line T. Let N be the rotation of point Z by angle 2pi/3 around point B. Point Q is the reflection of point M across line X. Point S is obtained by rotating point N by angle 11pi/12 about point Q. Point G is the reflection of point P across line X. Point I is the reflection of point B across point N. Point V is the midpoint of segment GS. Let E be the reflection of point N across point V. Find the distance between points E and I. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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UE = 11. Point A is obtained by rotating point E by angle 7pi/12 about point U. Point L is obtained by rotating point E by angle 2pi/3 about point U. Point H is the midpoint of segment LA. Let T be the midpoint of segment HE. Let D be the midpoint of segment HA. Find the distance between points D and T. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let JL = 3. JN = 5. Line K is the perpendicular bisector of segment LN. Point O is the reflection of point J across line K. Let V be the midpoint of segment JN. Point T is the reflection of point V across line K. Point W is the reflection of point O across point L. What is the length of segment TW? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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RY = 5. Let K be the midpoint of segment YR. Let F be the angle bisector of angle YKR. Point O is the midpoint of segment RK. Let S be the line through point R parallel to line F. Let I be the reflection of line F across line S. Point Q is the reflection of point R across line I. Find the distance between points Q and O. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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PD = 12. Let Q be the perpendicular bisector of segment DP. Point L is obtained by rotating point P by angle 5pi/12 about point D. Line O is the angle bisector of angle PLD. Point B is the reflection of point L across line Q. Let N be the midpoint of segment LD. Point K is the reflection of point N across line O. Find the length of segment BK. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let TF = 12. Let W be the reflection of point F across point T. Let S be the line through points T and F. Line X passes through point W perpendicular to line S. Point I is on line X with |IT| = 8. Let C be the reflection of point W across point F. Let A be the midpoint of segment IT. Point L is the midpoint of segment TC. Point J is the midpoint of segment LF. Let R be the midpoint of segment JF. What is the length of segment RA? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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GJ = 2. Line V passes through points J and G. Let X be the reflection of point G across point J. Line N is the perpendicular bisector of segment JG. Point E lies on line V. Point Q is the reflection of point E across point G. Point F is on line N with |FX| = 11. Let A be the angle bisector of angle QJF. Let I be the perpendicular bisector of segment XJ. Point W is the reflection of point F across line I. Point Z is the reflection of point W across line A. Point C is the reflection of point G across point F. Let H be the midpoint of segment ZC. What is the distance between points H and Z? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let IF = 7. Let J be the rotation of point F by angle 11pi/12 around point I. Line T passes through point F perpendicular to segment IF. Let X be the line through point I parallel to line T. Point U is obtained by rotating point J by angle 7pi/12 about point F. Point G is the reflection of point U across line T. Point W is on line X. Point V is the midpoint of segment WU. Line O passes through point V perpendicular to line X. Point Y is the intersection of segments IG and JU. Let B be the midpoint of segment YF. Point S is the reflection of point W across line O. Find the length of segment SB. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let JS = 9. Let K be the reflection of point J across point S. Let Z be the rotation of point K by angle 3pi/4 around point S. Let Y be the reflection of point K across point Z. Let N be the angle bisector of angle SKY. Let V be the reflection of line N through point S. Point O is the reflection of point Z across line V. Find the distance between points O and Z. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let DO = 7. Point J is obtained by rotating point D by angle pi/3 about point O. Point L lies on segment OJ. Line P is the angle bisector of angle DOL. Let X be the reflection of line P through point J. Line T passes through point D parallel to segment OJ. Lines X and T intersect at point A. Let S be the reflection of point O across point A. What is the distance between points S and A? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let VG = 6. Let F be the rotation of point G by angle pi/2 around point V. Point A is obtained by rotating point G by angle 7pi/12 about point F. Let S be the midpoint of segment FV. Point T is the midpoint of segment AF. Let H be the midpoint of segment TS. Point E is the reflection of point H across point G. Point Y is the reflection of point E across segment FV. Find the length of segment EY. Express your answer as a decimal number rounded to 2 decimal places.

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OM = 10. Point Q is the reflection of point M across point O. Let U be the perpendicular bisector of segment MO. Point P is the reflection of point Q across line U. Let Z be the perpendicular bisector of segment PM. Point S is the reflection of point O across line Z. Find the distance between points P and S. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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UB = 7. Let M be the rotation of point B by angle pi/12 around point U. Point V is the reflection of point M across point U. Point D is the reflection of point B across segment UM. Let R be the midpoint of segment VU. Let T be the reflection of point R across point D. Let F be the perpendicular bisector of segment UM. Point E is the reflection of point V across line F. Let P be the line through point B perpendicular to line F. Point H is the reflection of point E across line P. What is the distance between points T and H? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let UC = 1. Point L is obtained by rotating point C by angle 2pi/3 about point U. Let T be the midpoint of segment UL. Let N be the rotation of point L by angle pi/4 around point T. Let I be the perpendicular bisector of segment TC. Point H lies on line I. Point A is the reflection of point U across segment HN. What is the length of segment NA? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let FH = 3. Line W is the perpendicular bisector of segment FH. Let U be the midpoint of segment HF. Point X is on line W with |XU| = 2. Let P be the midpoint of segment HU. Let G be the angle bisector of angle FUX. Point I is the reflection of point X across line G. Line O passes through point P perpendicular to line G. Point M is the reflection of point I across line O. Let D be the reflection of point M across point H. What is the length of segment MD? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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ZW = 2. Let C be the rotation of point W by angle pi/6 around point Z. Point T is the midpoint of segment CZ. Point D is the reflection of point T across segment CW. Let F be the line through point Z parallel to segment CW. Point X is obtained by rotating point Z by angle pi/12 about point T. Let H be the rotation of point X by angle pi around point C. Line S passes through points W and H. Point M is the midpoint of segment CW. Point U is the reflection of point X across line F. Point R is the midpoint of segment TH. Line E passes through points U and R. Line G is the reflection of line E across point M. Point J is the reflection of point U across line S. Line K passes through point D perpendicular to line G. Point Y is the reflection of point W across line K. What is the length of segment JY? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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JP = 12. Let V be the rotation of point P by angle pi/3 around point J. Point D is the midpoint of segment JP. Point K is the midpoint of segment VP. Let A be the rotation of point D by angle 5pi/12 around point V. Point U is the midpoint of segment KJ. Let B be the reflection of point U across point A. Let G be the perpendicular bisector of segment UB. Let M be the line through point P parallel to line G. Point H is the reflection of point D across line M. Let E be the reflection of point V across point U. Line O passes through points A and E. Let T be the reflection of point K across point H. Point Q is the reflection of point J across line O. Find the length of segment TQ. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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OC = 11. Point P is the reflection of point O across point C. Line J passes through point O perpendicular to segment PO. Point U is the midpoint of segment CO. Let H be the reflection of point P across point O. Let B be the perpendicular bisector of segment PO. Let I be the reflection of point H across point C. Let A be the rotation of point O by angle pi/6 around point I. Let V be the midpoint of segment CA. Let T be the line through point V parallel to line B. Point E is the reflection of point V across line J. Point F is obtained by rotating point V by angle pi/2 about point E. Let Y be the reflection of point F across point H. Point W is the reflection of point A across segment PO. Let X be the line through point U parallel to segment YW. Segment PO and line T intersect at point K. Line L passes through point F parallel to segment YW. Let D be the reflection of line B across line L. Line R is the reflection of line D across point H. Point M is the intersection of lines X and R. Find the distance between points M and K. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let LK = 2. Line W is the perpendicular bisector of segment LK. Point P is obtained by rotating point K by angle 11pi/12 about point L. Line D is the perpendicular bisector of segment LP. Let Z be the reflection of line W through point K. Let X be the reflection of line Z across line W. Let Y be the reflection of line W across line D. Point S is the intersection of lines Z and Y. Let I be the line through points K and S. Lines X and I intersect at point N. What is the distance between points S and N? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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SB = 1. Let X be the midpoint of segment SB. Point D is the midpoint of segment BX. Let I be the midpoint of segment BD. Let O be the rotation of point S by angle pi/6 around point X. Line G passes through points X and D. Line T passes through points B and O. Let Q be the reflection of line G across line T. Point U is the reflection of point I across line Q. What is the length of segment UO? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let NM = 12. Point F is obtained by rotating point M by angle pi/2 about point N. Let W be the vector from point N to point M. Let J be the perpendicular bisector of segment NM. Let X be the line through point N perpendicular to line J. Point P is the reflection of point F across line X. Let D be point P translated by vector W. Line O is the perpendicular bisector of segment MF. Point Q is the reflection of point D across line O. Let K be the midpoint of segment PN. Point R is the reflection of point K across point Q. Point L is the midpoint of segment QR. Find the length of segment LR. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let IG = 6. Let U be the midpoint of segment GI. Let B be the rotation of point G by angle pi/3 around point I. Let M be the vector from point G to point B. Let D be the line through points I and U. Point O is the midpoint of segment GB. Let H be point O translated by vector M. Point K is the reflection of point B across line D. Let V be the rotation of point K by angle pi/2 around point B. Point X is the reflection of point U across segment HB. Point W is the midpoint of segment XV. Let Y be the midpoint of segment WG. Let N be the reflection of point Y across point U. Find the length of segment NV. Express your answer as a decimal number rounded to 2 decimal places.

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[User]
Let BX = 6. Let I be the reflection of point B across point X. Let J be the rotation of point I by angle 2pi/3 around point B. Point D is the reflection of point J across segment BX. Let C be the line through points D and I. Point Q is the reflection of point B across line C. Let Z be the midpoint of segment QX. Point O is the midpoint of segment BD. Point V is the reflection of point Z across segment BD. What is the distance between points V and O? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let VH = 5. Let X be the rotation of point H by angle 5pi/12 around point V. Let L be the reflection of point H across point V. Let R be the line through points X and V. Point Y is the reflection of point X across segment HV. Let D be the perpendicular bisector of segment LX. Let A be the reflection of line D across line R. Line B passes through point X parallel to line A. Let Q be the reflection of line R across line A. Point S is the intersection of lines B and Q. Line P passes through point Y perpendicular to segment HV. Point C is the reflection of point S across segment HV. Point Z is the reflection of point C across line P. What is the distance between points V and Z? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let ZD = 3. Let S be the rotation of point D by angle 11pi/12 around point Z. Let F be the angle bisector of angle ZDS. Point M is the reflection of point D across point S. Point E is the reflection of point M across point D. Point H is the reflection of point S across line F. Point K is the reflection of point E across segment HS. Find the length of segment KH. Express your answer as a decimal number rounded to 2 decimal places.

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[User]
Let EF = 6. Let W be the perpendicular bisector of segment FE. Let I be the midpoint of segment FE. Let G be the rotation of point F by angle 7pi/12 around point I. Point N is the midpoint of segment GE. Point Z is the reflection of point N across point G. Let H be the line through point I parallel to segment GZ. Point J is the reflection of point G across line W. Point C is the reflection of point Z across segment FE. Point R is the reflection of point N across line H. Let A be the midpoint of segment RC. Find the distance between points A and J. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
ZR = 3. Let I be the rotation of point R by angle pi/4 around point Z. Point K is the reflection of point R across point I. Point G is obtained by rotating point R by angle 5pi/12 about point I. Point A is the midpoint of segment IG. Let D be the rotation of point A by angle pi/4 around point I. Point W is the midpoint of segment DI. Let V be the midpoint of segment KW. Point S is the midpoint of segment GV. Find the distance between points S and V. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let ZA = 8. Let V be the rotation of point Z by angle 7pi/12 around point A. Let I be the midpoint of segment AV. Line S is the angle bisector of angle AZI. Point X is the reflection of point I across line S. Let N be the reflection of point Z across point V. Point K is the reflection of point A across segment VN. What is the length of segment KX? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let AB = 10. Let E be the perpendicular bisector of segment BA. Point F is obtained by rotating point A by angle pi/4 about point B. Point O lies on line E at distance 3 from point F. Let Q be the reflection of point A across point B. Point L lies on line E at distance 7 from point O. Let W be the reflection of point O across point F. Let N be the midpoint of segment WL. Let J be the perpendicular bisector of segment AN. Point G is the reflection of point Q across line J. Find the distance between points N and G. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
XZ = 10. Point D is the reflection of point X across point Z. Line E is the angle bisector of angle ZXD. Let P be the rotation of point Z by angle 2pi/3 around point X. Line L passes through point P perpendicular to line E. Point I is the reflection of point D across line L. Let U be the reflection of point X across point I. Let F be the reflection of point X across point U. Let V be the midpoint of segment FP. Find the distance between points V and F. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let JW = 12. Point N is obtained by rotating point J by angle pi/12 about point W. Let B be the midpoint of segment NJ. Point S is the midpoint of segment WJ. Let D be the reflection of point W across point B. Find the length of segment SD. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
HK = 8. Let B be the perpendicular bisector of segment HK. Let W be the reflection of point H across point K. Point O lies on line B at distance 6 from point K. Let J be the reflection of point W across point O. Let M be the line through point O perpendicular to line B. Point R is the midpoint of segment JO. Point N is the reflection of point H across line M. Let V be the midpoint of segment NR. Find the distance between points V and R. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let TZ = 8. Point H is the midpoint of segment TZ. Point M is obtained by rotating point Z by angle 2pi/3 about point H. Let C be the reflection of point M across point H. Let G be the line through points M and Z. Point P is the reflection of point H across line G. Point B is the reflection of point H across point C. What is the distance between points P and B? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
AB = 2. Point O is obtained by rotating point A by angle pi/12 about point B. Let W be the vector from point B to point O. Let L be the angle bisector of angle BOA. Point M is the translation of point A by vector W. Let I be the line through points M and O. Let R be the reflection of line I across line L. Point T is the midpoint of segment BO. Let J be the line through point T perpendicular to line R. Point P is the reflection of point A across line J. Let Q be the midpoint of segment PA. What is the length of segment OQ? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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EW = 11. Point G is the reflection of point W across point E. Let S be the rotation of point E by angle pi/3 around point W. Let Y be the midpoint of segment GE. Let C be the reflection of point G across point S. Let B be the vector from point E to point C. Point U is the translation of point S by vector B. Line P passes through points Y and S. Let R be the angle bisector of angle UGW. Let K be the reflection of line R across line P. Point I is obtained by rotating point C by angle 5pi/12 about point W. Let D be the perpendicular bisector of segment UW. Point X is the reflection of point I across segment UW. Line Q passes through point X parallel to line D. Lines Q and K intersect at point N. Find the length of segment NG. Express your answer as a decimal number rounded to 2 decimal places.

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CB = 1. Line A is the perpendicular bisector of segment BC. Let Q be the line through point C perpendicular to segment BC. Point P lies on line A at distance 8 from point B. Point M is the reflection of point P across segment BC. Point J is the reflection of point P across line Q. Point O is the midpoint of segment PJ. Let W be the perpendicular bisector of segment JO. Point H is the reflection of point M across line W. Let D be the midpoint of segment MB. What is the length of segment DH? Express your answer as a decimal number rounded to 2 decimal places.

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[User]
OE = 12. Let Q be the midpoint of segment EO. Point N is the reflection of point Q across point E. Point A is the reflection of point E across point N. Let X be the reflection of point A across point Q. What is the distance between points X and A? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
CI = 1. Point H is obtained by rotating point I by angle 2pi/3 about point C. Point U is the reflection of point H across point C. Point D is obtained by rotating point C by angle pi/6 about point I. Let R be the reflection of point C across point I. Line N passes through points R and C. Let Z be the midpoint of segment ID. Let E be the line through point Z parallel to line N. Point M is the reflection of point D across line E. Point B is the reflection of point M across segment ID. Let P be the midpoint of segment RB. Find the distance between points U and P. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
QE = 5. Let K be the midpoint of segment EQ. Point J is obtained by rotating point Q by angle 2pi/3 about point E. Point M is obtained by rotating point E by angle 2pi/3 about point J. Let R be the rotation of point K by angle pi/2 around point M. Let Y be the midpoint of segment KR. Point V is the reflection of point Q across point M. Line T is the angle bisector of angle VQE. Line S is the reflection of line T across point M. Point N is the reflection of point Y across point R. Point P is the reflection of point J across line S. Find the distance between points P and N. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
ES = 7. Point A is obtained by rotating point S by angle 5pi/12 about point E. Let X be the line through points S and A. Point Y is the reflection of point A across segment SE. Point I is the midpoint of segment SE. Line W passes through point A perpendicular to line X. Point N is the reflection of point I across line W. Let D be the line through points Y and N. Point L is the reflection of point Y across line X. Point C is the reflection of point L across line D. Point P is the intersection of segments SE and CL. What is the distance between points N and P? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let HV = 8. Let T be the midpoint of segment VH. Point E is obtained by rotating point T by angle pi/6 about point V. Let M be the rotation of point T by angle pi/2 around point H. Let X be the reflection of point H across point M. Point J is the midpoint of segment EX. Point I is the reflection of point J across point X. Point Q is the midpoint of segment ME. Find the distance between points Q and I. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
RZ = 11. Point Q is the midpoint of segment RZ. Let F be the rotation of point Q by angle 7pi/12 around point R. Point A is the reflection of point R across point Z. Let L be the reflection of point A across point Q. Let W be the reflection of point F across point R. Let U be the rotation of point Q by angle 5pi/12 around point Z. Point G is the reflection of point F across segment LQ. Point J is the midpoint of segment UG. Point N is the midpoint of segment WJ. Point Y is the midpoint of segment GN. Find the distance between points N and Y. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
YW = 10. Point E is obtained by rotating point Y by angle 11pi/12 about point W. Let P be the midpoint of segment YE. Let K be the angle bisector of angle EPW. Point T is the reflection of point E across line K. Let Q be the line through point T perpendicular to line K. Let C be the angle bisector of angle PET. Line H passes through points E and W. Let U be the reflection of line H across line C. Line S is the reflection of line Q across line U. Let M be the reflection of line K through point E. Line L is the reflection of line M across line S. Point X is the reflection of point P across line L. What is the length of segment PX? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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OD = 7. Point H is obtained by rotating point D by angle pi/4 about point O. Point X is the reflection of point H across point D. Line M passes through points X and H. Point G is the reflection of point O across line M. Point C is the reflection of point G across point O. Find the distance between points C and H. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
WP = 6. Point M is the midpoint of segment WP. Point I is obtained by rotating point P by angle pi/12 about point M. Point B is the midpoint of segment IM. Let U be the reflection of point B across point M. Let X be the angle bisector of angle UMB. Point S is the midpoint of segment PU. Point R is the reflection of point S across line X. Point A is the midpoint of segment RM. Point K is the midpoint of segment UA. Point O is the reflection of point W across line X. Find the length of segment KO. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
PU = 3. Let Z be the rotation of point U by angle pi/6 around point P. Let O be the rotation of point P by angle pi/2 around point U. Let T be the reflection of point Z across point O. Point Y is the midpoint of segment OU. Point A is the reflection of point Z across point U. Let C be the midpoint of segment TO. Let M be the line through points A and O. Point K is the reflection of point T across line M. Let J be the line through points Y and T. Let R be the line through point K parallel to line M. Lines J and R intersect at point S. Point I is the reflection of point C across line R. Let F be the midpoint of segment IC. Let W be the midpoint of segment SF. Find the distance between points W and F. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let LB = 12. Point O is the midpoint of segment LB. Point A is the reflection of point O across point L. Let T be the perpendicular bisector of segment AL. Let G be the line through point O parallel to line T. Let H be the rotation of point L by angle 2pi/3 around point O. Let V be the reflection of line T across line G. Let P be the line through points O and H. Point D is the midpoint of segment LH. Line K is the reflection of line P across point L. Point X is the reflection of point L across line P. Point R is the reflection of point D across line P. Let Q be the reflection of line V through point L. Point U is the reflection of point X across line K. Point E is the reflection of point D across line V. Let J be the midpoint of segment XR. Point Y is the intersection of segment JU and line Q. Find the distance between points E and Y. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let VS = 10. Point C is the reflection of point S across point V. Let B be the midpoint of segment SV. Let G be the rotation of point S by angle pi/12 around point B. Point L is the reflection of point G across segment BS. Point H is the midpoint of segment CG. Line M is the perpendicular bisector of segment CV. Point Z is the reflection of point L across line M. Find the distance between points Z and H. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let OW = 11. Line Y is the perpendicular bisector of segment OW. Line P passes through point W parallel to line Y. Point T is the reflection of point O across line P. Point V is the reflection of point W across point T. Line A passes through points W and T. Let U be the rotation of point V by angle 5pi/6 around point W. Let S be the rotation of point O by angle pi/6 around point U. Let C be the midpoint of segment UO. Let R be the rotation of point V by angle 5pi/12 around point C. Let F be the reflection of point C across point W. Line G passes through point R perpendicular to line A. Point L is the reflection of point F across line A. Point I is the reflection of point L across line G. Find the distance between points I and S. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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SZ = 6. Let A be the perpendicular bisector of segment SZ. Line K passes through point S parallel to line A. Point U lies on line K. Let W be the midpoint of segment SU. Let G be the reflection of point W across point Z. Point X is the reflection of point G across line K. What is the distance between points G and X? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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Let NF = 1. Let H be the rotation of point F by angle 11pi/12 around point N. Let I be the midpoint of segment HN. Let D be the rotation of point I by angle 5pi/6 around point H. Let S be the midpoint of segment HD. Point G is the midpoint of segment SN. Point T is the midpoint of segment DG. Let M be the midpoint of segment GT. What is the length of segment MN? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let IX = 2. Point D is the midpoint of segment IX. Let C be the rotation of point I by angle 2pi/3 around point D. Point U is obtained by rotating point X by angle 11pi/12 about point D. Let M be the midpoint of segment XC. Point S is the midpoint of segment DI. Point N is the reflection of point X across segment SM. Let L be the midpoint of segment MN. Point H is the reflection of point U across segment IX. Find the length of segment HL. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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LX = 5. Let S be the midpoint of segment XL. Let T be the rotation of point L by angle 5pi/6 around point X. Line F passes through point T perpendicular to segment LX. Let P be the line through point T perpendicular to line F. Let O be the reflection of point S across point X. Point N is the reflection of point L across line P. Let M be the perpendicular bisector of segment LO. Let Y be the reflection of line M through point T. Point B is the reflection of point N across line Y. Find the distance between points S and B. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let CS = 5. Let B be the perpendicular bisector of segment CS. Line N passes through point C parallel to line B. Let G be the rotation of point S by angle 11pi/12 around point C. Let K be the rotation of point G by angle pi around point S. Point M is the reflection of point C across point K. Point Z is the reflection of point K across segment MG. Line N and segment MG intersect at point P. Find the length of segment PZ. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let XT = 4. Line I is the perpendicular bisector of segment XT. Let F be the rotation of point T by angle pi/6 around point X. Line K passes through point F perpendicular to line I. Point B is the reflection of point T across point X. Let P be the reflection of point F across point B. Let H be the midpoint of segment BX. Let A be the midpoint of segment HP. Point R is the reflection of point T across line K. Point G is the reflection of point R across point A. Point Y is the reflection of point F across segment HP. What is the length of segment GY? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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GV = 1. Point H is obtained by rotating point G by angle pi/2 about point V. Let W be the midpoint of segment GV. Line X is the angle bisector of angle HWV. Point D is obtained by rotating point W by angle 5pi/12 about point G. Line O passes through point H parallel to line X. Point F is the midpoint of segment DV. Let Z be the midpoint of segment WF. Let L be the reflection of line O across line X. Point Q is the reflection of point F across line L. Let N be the reflection of point Z across point G. Let J be the midpoint of segment DN. Find the length of segment JQ. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


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JB = 12. Let F be the reflection of point B across point J. Let G be the perpendicular bisector of segment BJ. JI = 11. Line H passes through point J perpendicular to segment BJ. Point U is the reflection of point I across line H. Let O be the reflection of point U across point B. Point P is the reflection of point O across line G. Let R be the midpoint of segment FP. Find the length of segment FR. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
QU = 6. Let R be the rotation of point Q by angle 5pi/6 around point U. Let B be the midpoint of segment UR. Line F is the perpendicular bisector of segment QU. Point A is the reflection of point B across line F. Let C be the midpoint of segment BU. Point J is the reflection of point R across segment BA. Find the distance between points C and J. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let AC = 3. Point F is the reflection of point C across point A. Let K be the midpoint of segment AC. Point N is obtained by rotating point F by angle 5pi/12 about point K. Let Z be the rotation of point F by angle pi/12 around point C. Line D passes through points Z and N. Let W be the reflection of point A across point Z. Point T is the reflection of point C across segment ZW. Let B be the midpoint of segment TZ. Point Q is the reflection of point T across line D. Let Y be the midpoint of segment TB. Let P be the reflection of point A across point Q. What is the distance between points P and Y? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
ZI = 6. ZD = 12. Let L be the midpoint of segment DZ. Let O be the vector from point L to point D. Point H is obtained by rotating point D by angle pi/6 about point L. Point B is the translation of point I by vector O. Let W be the line through points Z and B. Line A passes through point H parallel to line W. Let J be the line through point D perpendicular to line A. Point U is the reflection of point H across line J. Point M is the reflection of point D across line W. Point F is the reflection of point D across segment MU. Find the distance between points U and F. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let FJ = 10. Let O be the rotation of point F by angle 5pi/12 around point J. Let Z be the midpoint of segment JO. Let R be the midpoint of segment JZ. Let Y be the midpoint of segment RF. What is the distance between points Y and Z? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let YR = 2. Let W be the midpoint of segment YR. Point L is obtained by rotating point W by angle pi/12 about point R. Line X is the perpendicular bisector of segment WL. Line K is the reflection of line X across point Y. Let H be the rotation of point W by angle 5pi/6 around point Y. Let F be the line through point Y perpendicular to line K. Point N is the midpoint of segment RW. Point P is the reflection of point N across point W. Point D is obtained by rotating point H by angle 11pi/12 about point P. Point B is the reflection of point P across line F. Point V is the reflection of point B across segment RW. Line S is the angle bisector of angle PDV. Let E be the reflection of line S through point N. Point J is the midpoint of segment DH. Point C is the reflection of point J across line E. What is the distance between points W and C? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
IQ = 12. Let F be the rotation of point Q by angle 5pi/12 around point I. Point R is the midpoint of segment IQ. Point L is obtained by rotating point Q by angle 2pi/3 about point R. Line T is the angle bisector of angle QRL. Let J be the reflection of point Q across point I. Point O is the reflection of point F across line T. Let C be the vector from point J to point I. Let W be point F translated by vector C. Let B be the line through point O perpendicular to line T. Let V be the perpendicular bisector of segment QI. Point X is the reflection of point F across line V. Line U passes through point W parallel to line B. Point E is the reflection of point X across line U. Point M is the midpoint of segment EX. Find the distance between points M and X. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let ZP = 3. Point H is the reflection of point Z across point P. Line N is the perpendicular bisector of segment ZH. Point T lies on line N at distance 9 from point H. Let G be the reflection of point T across point P. Let E be the reflection of point G across point T. Let B be the midpoint of segment EZ. What is the length of segment GB? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
BU = 12. Line D is the perpendicular bisector of segment UB. Let G be the midpoint of segment UB. Let I be the midpoint of segment GB. Line T is the perpendicular bisector of segment GB. Point M is the midpoint of segment UI. Let V be the line through point B parallel to line T. Let Q be the rotation of point G by angle 11pi/12 around point M. Point E is the reflection of point Q across point M. Point C is the reflection of point Q across line V. Line J is the reflection of line D across point E. Let S be the angle bisector of angle CEM. Point O is the reflection of point C across line S. Let X be the angle bisector of angle GOM. Line W is the reflection of line X across point G. Point L is the intersection of lines J and W. Point R is the reflection of point L across line X. What is the length of segment QR? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
UK = 5. Point E is on segment UK. Point C is the midpoint of segment EK. T is constructed so that KT = 3. Let V be the midpoint of segment CK. Let Q be the reflection of point T across point V. Point Z is the reflection of point C across segment TQ. Find the length of segment QZ. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
RD = 9. Let K be the reflection of point D across point R. Point W is obtained by rotating point D by angle 3pi/4 about point K. Line P passes through points W and D. Line H is the perpendicular bisector of segment KW. Point M is the reflection of point K across point D. Let A be the line through point R parallel to line H. Point E is the reflection of point M across point W. Point L is the intersection of lines A and P. Find the distance between points L and E. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let IF = 9. Point H is obtained by rotating point F by angle 5pi/6 about point I. Let R be the rotation of point F by angle pi around point I. Let G be the midpoint of segment IH. Let B be the reflection of point G across point R. Point Q is obtained by rotating point H by angle pi/4 about point R. Let D be the rotation of point Q by angle pi/6 around point B. Let P be the reflection of point R across point Q. Line Z passes through points P and I. Point W is the reflection of point R across line Z. Line U is the perpendicular bisector of segment DW. Point L is the midpoint of segment IB. Point A is the reflection of point F across line U. Point J is the reflection of point L across line U. Find the length of segment JA. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
NV = 8. Let D be the perpendicular bisector of segment VN. Let U be the vector from point V to point N. Let X be the rotation of point V by angle 5pi/12 around point N. Line B passes through points N and X. Point J is the translation of point N by vector U. Point Y is the reflection of point J across line D. Line S is the reflection of line D across line B. Point I is the reflection of point Y across line B. Lines S and B intersect at point O. Point G is the reflection of point Y across point O. What is the distance between points G and I? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
RB = 1. Let T be the rotation of point R by angle 7pi/12 around point B. Line A is the angle bisector of angle RBT. Point G is obtained by rotating point R by angle 11pi/12 about point T. Point L is the reflection of point R across point G. Point K is the reflection of point G across line A. Let Y be the line through points T and K. Point S is the reflection of point L across point K. Let M be the reflection of line Y through point R. Point F is the reflection of point S across line M. What is the distance between points L and F? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let CP = 12. Point E is obtained by rotating point C by angle pi/4 about point P. Let N be the rotation of point E by angle 11pi/12 around point P. Line G is the angle bisector of angle NEC. Point X is the reflection of point P across line G. Let M be the reflection of point X across point E. Point Y is the midpoint of segment PC. Let W be the midpoint of segment MY. Find the distance between points W and M. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
KL = 3. Line Q passes through points L and K. Let J be the rotation of point L by angle 11pi/12 around point K. Point D is the reflection of point J across point L. Line W is the angle bisector of angle KDJ. Line P is the reflection of line Q across line W. Point V is obtained by rotating point J by angle pi/3 about point K. Point X is obtained by rotating point L by angle pi/3 about point K. Line M is the perpendicular bisector of segment VX. Point O is the reflection of point L across line P. Let U be the reflection of point D across point J. Point E is the midpoint of segment UX. Point C is the reflection of point J across line M. Let H be the angle bisector of angle KLE. Point F is the reflection of point C across line H. Find the distance between points F and O. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
TX = 7. Let U be the vector from point T to point X. Let O be point X translated by vector U. Let V be the reflection of point O across point T. Point Y is obtained by rotating point O by angle pi/4 about point X. Let C be point O translated by vector U. Point M is the reflection of point V across point Y. Let P be the midpoint of segment CY. Segments MT and CY intersect at point G. Find the distance between points G and P. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let MV = 1. Let Y be the reflection of point M across point V. Point L is the reflection of point V across point Y. Point X is the reflection of point V across point M. Line F is the perpendicular bisector of segment VL. Let W be the midpoint of segment YX. Point I is on line F with |IM| = 5. Point E is the reflection of point W across line F. Line Q passes through point I parallel to segment YX. Line T passes through point E perpendicular to segment YX. Point C is the reflection of point V across line T. Point P is the reflection of point C across line Q. Point H is the midpoint of segment EM. Point J is the reflection of point H across segment CI. Point S is the reflection of point P across segment EI. What is the length of segment SJ? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
PR = 12. Let F be the vector from point R to point P. Let O be the reflection of point P across point R. Point B is obtained by rotating point P by angle pi/12 about point O. Point X is the translation of point P by vector F. Let Z be the rotation of point B by angle 7pi/12 around point P. Point E is the midpoint of segment ZO. Point I is the reflection of point P across segment ZO. Point H is the reflection of point Z across segment RP. Point Q is the midpoint of segment HR. Let N be the reflection of point Q across point R. Let L be the reflection of point N across point I. Let W be the line through point E parallel to segment RP. Point D is the reflection of point X across line W. Find the distance between points L and D. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let WJ = 12. Let D be the rotation of point W by angle pi around point J. Line S is the angle bisector of angle DWJ. Line U passes through point J perpendicular to line S. Point M is on line U with |MJ| = 11. Let C be the perpendicular bisector of segment MD. Line I is the reflection of line C across point D. Point R is the midpoint of segment JD. Line P is the reflection of line C across line S. Let X be the reflection of line I across line P. Point L is the intersection of lines X and I. What is the distance between points R and L? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
QA = 6. Let N be the reflection of point A across point Q. Let C be the angle bisector of angle NQA. Let O be the line through point A parallel to line C. Line H is the reflection of line O across line C. Point U is the reflection of point A across line H. Point V is the reflection of point U across point Q. Let E be the perpendicular bisector of segment UN. Let Z be the rotation of point U by angle pi/12 around point Q. Let Y be the midpoint of segment VZ. Let T be the midpoint of segment QA. Point G is the reflection of point T across line E. Point X is the midpoint of segment TG. What is the distance between points Y and X? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let SE = 8. Point V is the midpoint of segment ES. Let D be the reflection of point V across point S. Point U is the midpoint of segment SV. Let Q be the perpendicular bisector of segment US. Point J is obtained by rotating point U by angle 11pi/12 about point V. Point C is the reflection of point D across line Q. Let P be the reflection of point C across point J. Point N is the midpoint of segment UP. Point H is the reflection of point C across segment UP. Let T be the midpoint of segment HN. What is the distance between points T and P? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
CD = 10. Let L be the rotation of point C by angle pi/4 around point D. Let W be the midpoint of segment DC. Let V be the reflection of point D across point L. Point I is the midpoint of segment LD. Let K be the reflection of point V across point I. Point T is the reflection of point W across point K. Point Z is the midpoint of segment LW. Point A is the midpoint of segment TD. Point Q is the reflection of point A across segment LW. Find the length of segment QZ. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let XO = 6. Point S is obtained by rotating point O by angle 7pi/12 about point X. Line Y is the perpendicular bisector of segment XS. Let V be the perpendicular bisector of segment SO. Let F be the rotation of point O by angle 3pi/4 around point S. Let A be the reflection of line V through point S. Point C is the reflection of point O across line Y. Let W be the midpoint of segment OF. Line U passes through points F and S. Line M is the reflection of line A across point C. Point Q is the reflection of point W across line U. Point D is the reflection of point Q across point F. Point P is the reflection of point D across line M. Point H is the reflection of point P across line Y. Point Z is the reflection of point P across line V. What is the distance between points H and Z? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
PA = 7. Point I is the midpoint of segment AP. Point B is the reflection of point A across point P. Point N is the midpoint of segment IA. Let T be the midpoint of segment IB. Line D is the perpendicular bisector of segment NB. Point G is on line D with |GI| = 9. Let U be the angle bisector of angle GTI. Point Y is the reflection of point N across line U. Point C is the reflection of point T across segment BG. Find the distance between points Y and C. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let QX = 11. Point B is the midpoint of segment QX. Let F be the reflection of point B across point Q. Point Y is obtained by rotating point X by angle pi/12 about point B. Point G is the midpoint of segment YB. Let C be the rotation of point Y by angle 11pi/12 around point F. Point A is obtained by rotating point X by angle 5pi/12 about point C. Point N is the reflection of point F across segment YG. Point K is obtained by rotating point N by angle pi/6 about point Y. Let R be the reflection of point G across point X. Point T is the reflection of point A across point R. Point M is the midpoint of segment KA. What is the length of segment TM? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
RT = 1. Let C be the rotation of point T by angle 11pi/12 around point R. Let L be the rotation of point C by angle 11pi/12 around point R. Point V is the reflection of point L across point C. Line O is the angle bisector of angle VTL. Let Y be the line through point L perpendicular to line O. Let N be the rotation of point R by angle 5pi/6 around point V. Point F is the reflection of point N across line Y. Let D be the midpoint of segment LN. Point H is the reflection of point F across segment CN. What is the length of segment DH? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let ZQ = 8. B is placed 7 units away from Q. Let C be the vector from point Q to point Z. Let I be the rotation of point B by angle pi around point Q. Point S is the translation of point I by vector C. Let H be the rotation of point Z by angle pi/3 around point Q. Point G is the reflection of point I across point H. Let F be the rotation of point Z by angle 3pi/4 around point H. Let Y be the midpoint of segment GS. Point A is the reflection of point F across segment SB. Line U is the perpendicular bisector of segment SB. Point K is the reflection of point A across line U. What is the length of segment KY? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
WA = 9. Line O is the perpendicular bisector of segment AW. Line D passes through point W parallel to line O. Point B is the reflection of point A across line D. Let X be the reflection of point B across point A. Let K be the reflection of point X across point B. Let U be the rotation of point A by angle 7pi/12 around point W. Point Z is obtained by rotating point A by angle 3pi/4 about point U. Point M is the reflection of point W across segment AZ. Let C be the midpoint of segment ZA. Let Q be the midpoint of segment CM. Let G be the reflection of point A across point Z. Let N be the midpoint of segment KG. Point V is the intersection of segments AZ and QN. What is the length of segment VX? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let FW = 6. Line G is the perpendicular bisector of segment WF. Line D is the reflection of line G across point W. Point T is on line G. Let C be the reflection of point F across point T. Point K is on line D with |KT| = 2. Point Q is the reflection of point K across line G. Let M be the reflection of point T across point Q. Line H passes through point F perpendicular to segment FW. Point N is the reflection of point F across point M. Point A is the reflection of point N across line H. Find the length of segment CA. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
NV = 8. W is placed 4 units away from V. Let NR = 8. Point A is the midpoint of segment RW. Point B is the midpoint of segment WN. Let G be the midpoint of segment AB. Let O be the midpoint of segment AG. What is the length of segment BO? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let SA = 2. Let F be the rotation of point A by angle 11pi/12 around point S. Let O be the midpoint of segment FA. Point V is the reflection of point S across point A. Point X is the reflection of point O across segment AS. Point B is the midpoint of segment XO. Find the distance between points B and V. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
SO = 3. Let J be the midpoint of segment OS. Point Q is the midpoint of segment JS. Point L is obtained by rotating point O by angle pi/12 about point Q. Point K is obtained by rotating point J by angle 5pi/12 about point Q. Point T is the midpoint of segment OK. Let M be the angle bisector of angle TLO. Line I passes through point T parallel to line M. Point E is the reflection of point K across line I. What is the length of segment TE? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
AM = 10. Point P is the reflection of point A across point M. Point X is the midpoint of segment AM. Let H be the midpoint of segment PM. Let W be the rotation of point H by angle pi around point A. Let V be the rotation of point X by angle 3pi/4 around point H. Let T be the angle bisector of angle VWH. Line D is the perpendicular bisector of segment XA. Line L is the reflection of line D across line T. Point U is the reflection of point P across point W. Point Q is the reflection of point M across line L. Point O is obtained by rotating point U by angle 3pi/4 about point A. Point B is the reflection of point Q across segment WO. Point S is the reflection of point U across point A. Point K is the reflection of point B across line T. What is the distance between points K and S? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let TE = 3. Let H be the midpoint of segment TE. Let G be the vector from point T to point E. Point N is obtained by rotating point E by angle 2pi/3 about point H. Let L be the line through points E and H. Point A is the reflection of point E across point N. Point D is the midpoint of segment HT. Let M be the reflection of point N across point T. Point K is the translation of point M by vector G. Point Z is the reflection of point K across line L. Line X is the angle bisector of angle AMD. Let O be the midpoint of segment EZ. Point V is the reflection of point O across segment EM. Point W is the reflection of point V across line X. Find the length of segment VW. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
DA = 8. Let V be the reflection of point A across point D. Let Y be the reflection of point D across point V. Let O be the rotation of point D by angle pi/6 around point V. Let F be the perpendicular bisector of segment VO. Let E be the midpoint of segment OV. Point U is the reflection of point V across segment EA. Point L is the reflection of point Y across line F. Let N be the reflection of point Y across point U. What is the length of segment LN? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let CX = 2. Point P is the midpoint of segment XC. Let M be the midpoint of segment PX. Let D be the angle bisector of angle CPM. Let J be the midpoint of segment CP. Line I is the reflection of line D across point C. Line H is the reflection of line I across point J. Point T is the reflection of point C across line H. Find the distance between points C and T. Express your answer as a decimal number rounded to 2 decimal places.

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[User]
Let LV = 7. Point H is the reflection of point V across point L. Let F be the midpoint of segment LV. Point T is the midpoint of segment LH. Point R is obtained by rotating point T by angle 5pi/12 about point L. Point C is the midpoint of segment LR. Let Z be the rotation of point L by angle 3pi/4 around point V. Point G is the reflection of point C across point F. Let Y be the line through points Z and T. Point S is the intersection of line Y and segment LC. What is the length of segment GS? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
CF = 1. Let R be the rotation of point C by angle 2pi/3 around point F. Line Y is the angle bisector of angle CFR. Let I be the reflection of line Y through point C. Point N is the midpoint of segment FR. Let S be the midpoint of segment CN. Point H is the reflection of point N across line I. Find the length of segment SH. Express your answer as a decimal number rounded to 2 decimal places.

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[User]
Let OP = 2. Point M is the reflection of point P across point O. Let B be the reflection of point M across point P. Line S is the perpendicular bisector of segment PM. Line A passes through point M parallel to line S. Let Q be the reflection of point O across point P. Let C be the reflection of line A across line S. Line I passes through point B parallel to line A. Let V be the midpoint of segment QM. Point T is the midpoint of segment PV. Let L be the reflection of line C across line I. Point N is the midpoint of segment TO. Line F is the reflection of line L across point N. Point X is the reflection of point B across line F. What is the distance between points X and B? Express your answer as a decimal number rounded to 2 decimal places.

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[User]
Let WJ = 11. Let N be the midpoint of segment WJ. Point S is obtained by rotating point J by angle pi/6 about point W. Point P is the midpoint of segment NW. Let L be the reflection of point S across point P. Let I be the reflection of point L across point W. Find the measure of angle ISJ, in radians. Express your answer as a decimal number rounded to 2 decimal places.

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[User]
OG = 2. Point E is the midpoint of segment GO. Point N is obtained by rotating point O by angle 7pi/12 about point E. Let A be the perpendicular bisector of segment EN. Let B be the line through point O parallel to line A. Line H passes through point E perpendicular to line B. Let V be the rotation of point O by angle 2pi/3 around point N. Point D is obtained by rotating point E by angle pi/4 about point N. Point X is the reflection of point D across line H. Let P be the midpoint of segment XD. Let T be the angle bisector of angle NVP. Point S is the reflection of point P across line T. Find the distance between points S and P. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Let XJ = 5. Point Z is obtained by rotating point J by angle pi/3 about point X. Let B be the rotation of point J by angle 3pi/4 around point X. Point A is the reflection of point Z across point B. Point D is the midpoint of segment JB. Let Y be the perpendicular bisector of segment XZ. Point H is the reflection of point D across line Y. Find the distance between points H and A. Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
TF = 11. Let X be the reflection of point F across point T. Point M is obtained by rotating point F by angle 5pi/6 about point T. Line W is the angle bisector of angle FMX. Point B is the reflection of point X across line W. Let S be the reflection of point T across point M. Let R be the reflection of point S across point B. Let N be the midpoint of segment RB. What is the distance between points N and R? Express your answer as a decimal number rounded to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}