JBMO-SL 2006 Problem 10

Let $ABCD$ be a trapezoid inscribed in a circle $\mathcal{C}$ with $AB\parallel CD$ , $AB=2CD$ . Let $\{Q\}=AD\cap BC$ and let $P$ be the intersection of tangents to $\mathcal{C}$ at $B$ and $D$ . Calculate the area of the quadrilateral $ABPQ$ in terms of the area of the triangle $PDQ$ .