RMO 2023 K6

The diagonals $AC$ and $BD$ of a cyclic quadrilateral $ABCD$ meet at $P$ . The point $Q$ is chosen on the segment $BC$ so that $PQ$ is perpendicular to $AC$ . Prove that the line joining the centres of the circumcircles of triangles $APD$ and $BQD$ is parallel to $AD$ .