CGMO 2019 Problem 1

Let $ABCD$ be a cyclic quadrilateral with circumcircle $\odot O.$ The lines tangent to $\odot O$ at $A,B$ intersect at $L.$ $M$ is the midpoint of the segment $AB.$ The line passing through $D$ and parallel to $CM$ intersects $\odot (CDL)$ at $F.$ Line $CF$ intersects $DM$ at $K,$ and intersects $\odot O$ at $E$ (different from point $C$ ). Prove that $EK=DK.$