MathNet 2023-part-02 — 191 problems (EN–VI) Question 23

Let $ABCDE$ be a convex cyclic pentagon such that $AB = BD$. Let $P$ be the intersection point of the lines $(EB)$ and $(AC)$. Let $Q$ be the intersection point of the lines $(BC)$ and $(DE)$. Show that $(PQ)$ and $(AD)$ are parallel.