Question 20
$\omega_{1}$ and $\omega_{2}$ are two circles that are externally tangent to each other at the point $M$ and internally tangent to a circle $\omega_{3}$ at the points $K$ and $L$, respectively. Let $A$ and $B$ be the two points where the common tangent line at $M$ to $\omega_{1}$ and $\omega_{2}$ intersects $\omega_{3}$. Show that if $\angle K A B = \angle L A B$ then the line segment $A B$ is a diameter of $\omega_{3}$.
