BG-MO 2005 Problem 4

Let $ABC$ be a triangle with $AC\neq BC$ , and let $A^{\prime }B^{\prime }C$ be a triangle obtained from $ABC$ after some rotation centered at $C$ . Let $M,E,F$ be the midpoints of the segments $BA^{\prime },AC$ and $CB^{\prime }$ respectively. If $EM=FM$ , find $\widehat{EMF}$ .