Question 6
Let $ABC$ be an acute, non-isosceles triangle with circumcenter $O$. The tangents to $(O)$ at $B$ and $C$ meet at $T$. A line through $T$ meets segment $AB$ at $D$ and ray $CA$ at $E$. Let $M$ be the midpoint of $DE$, and suppose that $MA$ meets $(O)$ again at $K$. Prove that $(MKT)$ is tangent to $(O)$.