OMM 2020 Problem 2

Let $ABC$ be a triangle with incenter $I$ . The line $BI$ meets $AC$ at $D$ . Let $P$ be a point on $CI$ such that $DI=DP$ ( $P\ne I$ ), $E$ the second intersection point of segment $BC$ with the circumcircle of $ABD$ and $Q$ the second intersection point of line $EP$ with the circumcircle of $AEC$ . Prove that $\angle PDQ=90^\circ$ .

Proposed by Ariel García