RU-SPB 2010 Problem 97

Incircle of $ABC$ tangent $AB,AC,BC$ in $C_1,B_1,A_1$ . $AA_1$ intersect incircle in $E$ . $N$ is midpoint $B_1A_1$ . $M$ is symmetric to $N$ relatively $AA_1$ . Prove that $\angle EMC= 90$