RU-ALLRUSSIAN 2016 Problem 102

Diagonals $AC,BD$ of cyclic quadrilateral $ABCD$ intersect at $P$ .Point $Q$ is on $BC$ (between $B$ and $C$ ) such that $PQ \perp AC$ .Prove that the line passes through the circumcenters of triangles $APD$ and $BQD$ is parallel to $AD$ .(A.Kuznetsov)