Can u solve this??

Let $ABC$ be a triangle with $AB = AC$ . If $D$ is the mid point of $BC$ , $E$ the foot of perpendicular drawn from $D$ to $AC$ and $F$ the mid point of $DE$ , $AF$ and $BE$ are joined and meet at $M$ .

What is the measure of the angle $AMB$ ?

P.S. please post a pure geometrical proof of this (without use of coordinate geometry)