Let ABCD be a cyclic quadrilateral with circumcircle ⊙O. The lines tangent to ⊙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 ⊙(CDL) at F. Line CF intersects DM at K, and intersects ⊙O at E (different from point C).
Prove that EK=DK. geometrycyclic quadrilateral