APMO 2013 - Asian Pacific Mathematics Olympiad Question 5

Let $ABCD$ be a quadrilateral inscribed in a circle $\omega$, and let $P$ lie on the extension of $AC$ such that $PB,PD$ are tangent to $\omega$. The tangent at $C$ meets $PD$ at $Q$ and line $AD$ at $R$. Let $E$ be the second intersection of $AQ$ with $\omega$. Prove that $B,E,R$ are collinear.

Newly drawn configuration: