Question 89
Let $ABC$ be a triangle with $AB = AC$. Let $M$ be the midpoint of $BC$. Let circles with diameters $AC$, $BM$ intersect at points $M$, $P$. Let $MP$ intersect $AB$ at $Q$. Let $R$ be a point on $AP$ such that $QR \parallel BP$. Prove that $CP$ bisects $\angle RCB$.