Problem

Source: China Mathematical Olympiad 1992 problem4

Tags: geometry, circumcircle, parallelogram, geometric transformation, reflection, trapezoid, symmetry



A convex quadrilateral $ABCD$ is inscribed in a circle with center $O$. The diagonals $AC$, $BD$ of $ABCD$ meet at $P$. Circumcircles of $\triangle ABP$ and $\triangle CDP$ meet at $P$ and $Q$ ($O,P,Q$ are pairwise distinct). Show that $\angle OQP=90^{\circ}$.