[User]
Let QG = 11. Let B be the rotation of point G by angle 7pi/12 around point Q. Let H be the midpoint of segment GQ. Line E passes through point H perpendicular to segment GQ. Let R be the midpoint of segment HB. Point W is the reflection of point B across line E. What is the inradius of triangle GRW? Express your answer as a decimal number rounded to 2 decimal places.

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


[User]
DM = 3. Let U be the reflection of point D across point M. Point C is the reflection of point M across point U. Point N is obtained by rotating point C by angle pi/4 about point U. Let Y be the reflection of point N across point C. Point A is the reflection of point N across point U. Point R is the midpoint of segment DM. Find the circumradius of triangle AYR. Express your answer as a decimal number rounded to 2 decimal places.

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


[User]
XY = 12. Let A be the rotation of point Y by angle pi/4 around point X. Let U be the midpoint of segment YA. Let L be the incenter of triangle XYA. Point S is the midpoint of segment XY. Find the measure of angle LUS, in radians. Express your answer as a decimal number rounded to 2 decimal places.

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


[User]
YA = 4. Let D be the rotation of point Y by angle pi around point A. Point X is the midpoint of segment AD. Let H be the rotation of point A by angle pi/4 around point Y. Point Z is the reflection of point H across point A. Point B is the reflection of point H across point D. Let T be the orthocenter of triangle ZXH. Find the length of segment TB. Express your answer as a decimal number rounded to 2 decimal places.

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


[User]
Let RX = 8. Let M be the rotation of point X by angle pi/6 around point R. Let E be the reflection of point R across point X. Point N is the reflection of point M across segment RX. Point B is the reflection of point N across point M. Let C be the reflection of point R across point B. Find the circumradius of triangle ECM. Express your answer as a decimal number rounded to 2 decimal places.

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