Circle : Exercise (8.3)-Problem 11

Two circles intersect at $ \displaystyle A$ and $ \displaystyle B$. A point $ \displaystyle P$ is taken on one so that $ \displaystyle PA$ and $ \displaystyle PB$ cut the other at $ \displaystyle Q$ and $ \displaystyle R$ respectively. The tangents at $ \displaystyle Q$ and $ \displaystyle R$ meet the tangent at $ \displaystyle P$ in $ \displaystyle S$ and $ \displaystyle T$ respectively. Prove that 

$ \displaystyle \text{(a)}$ $ \displaystyle \angle TPR=\angle BRQ$, 

$ \displaystyle \text{(b)}$ $ \displaystyle PBQS$ is cyclic.