RU-SPB 2015 Problem 114

$ABCD$ is convex quadrilateral. Circumcircle of $ABC$ intersect $AD$ and $DC$ at points $P$ and $Q$ . Circumcircle of $ADC$ intersect $AB$ and $BC$ at points $S$ and $R$ . Prove that if $PQRS$ is parallelogram then $ABCD$ is parallelogram