Question 94
Let $ABC$ be a triangle with $\angle BAC=90^\circ$, circumcenter $O$, and incenter $I$. The angle bisector of $\angle BAC$ meets the circumcircle of $ABC$ at $A$ and $P$. Let $Q$ be the perpendicular projection of $P$ onto $AB$, and let $R$ be the perpendicular projection of $I$ onto $PQ$. Prove that the line $RO$ bisects the segment $CI$.