# 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.