CMOQR 2021 Problem 3

$ABCDE$ is a regular pentagon. Two circles $C_1$ and $C_2$ are drawn through $B$ with centers $A$ and $C$ respectively. Let the other intersection of $C_1$ and $C_2$ be $P$ . The circle with center $P$ which passes through $E$ and $D$ intersects $C_2$ at $X$ and $AE$ at $Y$ . Prove that $AX = AY$ .