CN-SMO 2008 Problem 6

Circle $I$ is the incircle of $\triangle ABC$ . Circle $I$ is tangent to sides $BC$ and $AC$ at $M,N$ respectively. $E,F$ are midpoints of sides $AB$ and $AC$ respectively. Lines $EF, BI$ intersect at $D$ . Show that $M,N,D$ are collinear.