CH-SMO 2021 Problem 2

Let $\triangle ABC$ be an acute triangle with $AB =AC$ and let $D$ be a point on the side $BC$ . The circle with centre $D$ passing through $C$ intersects $\odot(ABD)$ at points $P$ and $Q$ , where $Q$ is the point closer to $B$ . The line $BQ$ intersects $AD$ and $AC$ at points $X$ and $Y$ respectively. Prove that quadrilateral $PDXY$ is cyclic.