Question 49
Let $ABC$ be a triangle with incenter $I$. The incircle of the triangle is tangent to the sides $BC$ and $AC$ in points $D$ and $E$, respectively. Let $P$ denote the common point of lines $AI$ and $DE$, and let $M$ and $N$ denote the mid-points of sides $BC$ and $AB$, respectively. Prove that points $M$, $N$ and $P$ are collinear.