Question 145
Let $ABCD$ be a convex quadrilateral. The points $M$, $N$, $P$ and $Q$ divide the segments $[AB]$, $[BC]$, $[CD]$ and $[DA]$, respectively, in the same ratio. Prove that the lines $AC$, $BD$, $MP$ and $NQ$ are concurrent if and only if $ABCD$ is a parallelogram.