Question 5
Let $ABCD$ be a quadrilateral inscribed in a circle with center $O$. Let $\Delta_1,\Delta_2$ be the images of line $AB$ under reflections in the internal bisectors of $\angle CAD,\angle CBD$, respectively. Let $P$ be the intersection of $\Delta_1,\Delta_2$. Prove that $OP$ and $CD$ are perpendicular.