OMCC 2015 Problem 3

Let $ABCD$ be a cyclic quadrilateral with $AB<CD$ , and let $P$ be the point of intersection of the lines $AD$ and $BC$ .The circumcircle of the triangle $PCD$ intersects the line $AB$ at the points $Q$ and $R$ . Let $S$ and $T$ be the points where the tangents from $P$ to the circumcircle of $ABCD$ touch that circle.

(a) Prove that $PQ=PR$ .

(b) Prove that $QRST$ is a cyclic quadrilateral.