OMM 2016 Problem 1

Let $C_1$ and $C_2$ be two circumferences externally tangents at $S$ such that the radius of $C_2$ is the triple of the radius of $C_1$ . Let a line be tangent to $C_1$ at $P \neq S$ and to $C_2$ at $Q \neq S$ . Let $T$ be a point on $C_2$ such that $QT$ is diameter of $C_2$ . Let the angle bisector of $\angle SQT$ meet $ST$ at $R$ . Prove that $QR=RT$