Problem

Source: Ukrainian Geometry Olympiad 2017, IX p4 , XI p3

Tags: geometry, parallelogram, circumcircle, Circumcenter, right angle



Let $ABCD$ be a parallelogram and $P$ be an arbitrary point of the circumcircle of $\Delta ABD$, different from the vertices. Line $PA$ intersects the line $CD$ at point $Q$. Let $O$ be the center of the circumcircle $\Delta PCQ$. Prove that $\angle ADO = 90^o$.