RIOPLATENSE 2017 Problem 5

Let $ABC$ be a triangle and $I$ is your incenter, let $P$ be a point in $AC$ such that $PI$ is perpendicular to $AC$ , and let $D$ be the reflection of $B$ wrt circumcenter of $\triangle ABC$ . The line $DI$ intersects again the circumcircle of $\triangle ABC$ in the point $Q$ . Prove that $QP$ is the angle bisector of the angle $\angle AQC$ .