Question 152
Let $ABP$, $BCQ$, $CAR$ be three non-overlapping triangles erected outside of acute triangle $ABC$. Let $M$ be the midpoint of segment $AP$. Given that $\angle PAB = \angle CQB = 45^\circ$, $\angle ABP = \angle QBC = 75^\circ$, $\angle RAC = 105^\circ$, and $RQ^2 = 6CM^2$, compute $AC^2/AR^2$.