The convex pentagon $ABCDE$ is cyclic and $AB = BD$. Let point $P$ be the intersection of the diagonals $AC$ and $BE$. Let the straight lines $BC$ and $DE$ intersect at point $Q$. Prove that the straight line $PQ$ is parallel to the diagonal $AD$.
Problem
Source: Austrian Regional Competition For Advanced Students 2019, p2
Tags: geometry, Cyclic, parallel, equal segments