Question 108
$ABC$ is a triangle with circumcircle $\omega_1$ and $\widehat{C} = 2\widehat{B}$. A tangent line to $\omega_1$ at $A$ intersects $BC$ at $E$. Let $\omega_2$ be a circle passing through $B$ and tangent to $AC$ at $C$. This circle intersects $AB$ for the second time at $F$. A line through $E$ is tangent to $\omega_2$ at $K$ (where $BC$ lies between $A$ and $K$). Let $M$ be the midpoint of arc $BC$ of $\omega_1$ (not containing $A$). Prove that $MFAK$ is a cyclic quadrilateral.