ÖMO 2020 Problem 1

Let $ABCD$ be a convex cyclic quadrilateral with the diagonal intersection $S$ . Let further be $P$ the circumcenter of the triangle $ABS$ and $Q$ the circumcenter of the triangle $BCS$ . The parallel to $AD$ through $P$ and the parallel to $CD$ through $Q$ intersect at point $R$ . Prove that $R$ is on $BD$ .

(Karl Czakler)