IR-MO-R2 2016 Problem 2

Let $ABC$ be a triangle such that $\angle C=2\angle B$ and $\omega$ be its circumcircle. a tangent from $A$ to $\omega$ intersect $BC$ at $E$ . $\Omega$ is a circle passing throw $B$ that is tangent to $AC$ at $C$ . Let $\Omega\cap AB=F$ . $K$ is a point on $\Omega$ such that $EK$ is tangent to $\Omega$ ( $A,K$ aren't in one side of $BC$ ). Let $M$ be the midpoint of arc $BC$ of $\omega$ (not containing $A$ ). Prove that $AFMK$ is a cyclic quadrilateral.