IT-CESENATICO 1989 Problem 4

Points $A,M,B,C,D$ are given on a circle in this order such that $A$ and $B$ are equidistant from $M$ . Lines $MD$ and $AC$ intersect at $E$ and lines $MC$ and $BD$ intersect at $F$ . Prove that the quadrilateral $CDEF$ is inscridable in a circle.