MEMO 2019 Problem 6

Let $ABC$ be a right-angled triangle with the right angle at $B$ and circumcircle $c$ . Denote by $D$ the midpoint of the shorter arc $AB$ of $c$ . Let $P$ be the point on the side $AB$ such that $CP=CD$ and let $X$ and $Y$ be two distinct points on $c$ satisfying $AX=AY=PD$ . Prove that $X, Y$ and $P$ are collinear.

Proposed by Dominik Burek, Poland