RO-TST 2008 Problem 14

Let $ABCD$ be a convex quadrilateral and let $O \in AC \cap BD$ , $P \in AB \cap CD$ , $Q \in BC \cap DA$ . If $R$ is the orthogonal projection of $O$ on the line $PQ$ prove that the orthogonal projections of $R$ on the sidelines of $ABCD$ are concyclic.