Question 93
Let $ABC$ be a triangle with circumcircle $\Omega$ and circumcenter $O$. Let $S$ be the center of the circle tangent to $AB$ and $AC$ and internally tangent to $\Omega$ at $K$. The circle with diameter $AS$ meets $\Omega$ again at $T$. Let $M$ be the midpoint of $BC$. Prove that $K$, $T$, $M$, and $O$ are concyclic.