Question 92
Let $S$ be a point inside $\varangle p O q$, and let $k$ be a circle which contains $S$ and touches the legs $O p$ and $O q$ in points $P$ and $Q$ respectively. Straight line $s$ parallel to $O p$ from $S$ intersects $O q$ in a point $R$. Let $T$ be the point of intersection of the ray $P S$ and circumscribed circle of $\triangle S Q R$ and $T \neq S$. Prove that $O T \| S Q$ and $O T$ is a tangent of the circumscribed circle of $\triangle S Q R$.