KöMaL 2012 B4480

The escribed circle drawn to side $AB$ of a triangle ABC touches the lines of sides $AB$, $BC$ and $CA$ at the points $E$, $F$, $G$, respectively. The intersection of lines $AF$ and $BG$ is $H$. The inscribed circle of the triangle formed by the midlines of triangle ABC touches the side parallel to $AB$ at point $N$. Prove that the points $E$, $H$ and $N$ are collinear.