Question 5
Two circles $\omega_{1}$ and $\omega_{2}$ are tangent at $S$, with $\omega_{1}$ inside $\omega_{2}$. Let $O$ be the center of $\omega_{1}$. A chord $[AB]$ of $\omega_{2}$ is tangent to $\omega_{1}$ at $T$. Show that $(AO)$, the perpendicular to $(AB)$ through $B$, and the perpendicular to $(ST)$ through $S$ are concurrent.
