TH-TMO 2015 Problem 4

Let $\vartriangle ABC$ be a triangle with an obtuse angle $\angle ACB$ . The incircle of $\vartriangle ABC$ centered at $I$ is tangent to the sides $AB, BC, CA$ at $D, E, F$ respectively. Lines $AI$ and $BI$ intersect $EF$ at $M$ and $N$ respectively. Let $G$ be the midpoint of $AB$ . Show that $M, N, G, D$ lie on a circle.