Question 87
Let $ABC$ 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 the circumcircle of $ABD$ in $P$ and $Q$, where $Q$ is the point closer to $B$. The line $BQ$ intersects $AD$ in $X$ and $AC$ in $Y$. Prove that $PDXY$ is cyclic.