Question 2
Let five points on a circle be labelled $A$, $B$, $C$, $D$, and $E$ in clockwise order. Assume $A E = D E$ and let $P$ be the intersection of $A C$ and $B D$. Let $Q$ be the point on the line through $A$ and $B$ such that $A$ is between $B$ and $Q$ and $A Q = D P$. Similarly, let $R$ be the point on the line through $C$ and $D$ such that $D$ is between $C$ and $R$ and $D R = A P$. Prove that $P E$ is perpendicular to $Q R$.