NL-BXMO-TST 2020 Problem 4

Three different points $A,B$ and $C$ lie on a circle with center $M$ so that $| AB | = | BC |$ . Point $D$ is inside the circle in such a way that $\vartriangle BCD$ is equilateral. Let $F$ be the second intersection of $AD$ with the circle . Prove that $| F D | = | FM |$ .