Question 2
Let $ABCD$ be a parallelogram. The incircle of triangle $ABC$ touches its sides $AB$, $BC$ and $AC$ at points $M$, $N$ and $K$ respectively. The lines $MK$ and $CD$ intersect at $P$, the lines $NK$ and $AD$ intersect at $Q$. Prove that the points $B$, $E$ and $F$ are collinear, where $E$ and $F$ are the midpoints of $MP$ and $NQ$ respectively.