Question 51
Let $A, B, C, D$ and $E$ be five points, in this order, on a circle such that $A E = D E$. Let $P$ be the intersection point of $(A C)$ and $(B D)$. Let $Q$ be the point on the ray $[B A)$ such that $A Q = D P$. Let $R$ be the point on the ray $[C D)$ such that $D R = A P$. Prove that the lines $(P E)$ and $(Q R)$ are perpendicular.