MathNet 2020 — Math Olympiad Vault — Part 04 Question 25

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