Question 50
Let $M$, $N$ and $P$ be the points on the sides $AB$, $BC$ and $CA$ of the triangle $ABC$, such that the quadrilateral $CPMN$ is a parallelogram. The lines $AN$ and $MP$ meet at $R$, the lines $BP$ and $MN$ meet at $S$ and the lines $AN$ and $BP$ meet at $Q$. Let $T$ be the image of $Q$ under the orthogonal projection onto the side $AB$. Prove that the areas of the triangle $NQP$ and the quadrilateral $TSQR$ are equal.