KMO 2023 Problem 1

In a triangle $ABC ~(\overline{AB} < \overline{AC})$ , points $D (\neq A, B)$ and $E (\neq A, C)$ lies on side $AB$ and $AC$ respectively. Point $P$ satisfies $\overline{PB}=\overline{PD}, \overline{PC}=\overline{PE}$ . $X (\neq A, C)$ is on the arc $AC$ of the circumcircle of triangle $ABC$ not including $B$ . Let $Y (\neq A)$ be the intersection of circumcircle of triangle $ADE$ and line $XA$ . Prove that $\overline{PX} = \overline{PY}$ .