Question 130
Four points $P$, $Q$, $R$ and $S$ lie in this order on a circle such that $\angle P S R = 90^\circ$. Let $H$ and $K$ be the feet of the perpendiculars from $Q$ to $P R$ and $P S$, respectively. Let $T$ be the intersection point of $H K$ and $Q S$. Prove that $|S T| = |T Q|$.