Question 35
Let $\triangle ABC$ be a triangle and the points $K$ and $L$ on $AB$, $M$ and $N$ on $BC$ and $P$ and $Q$ on $CA$ are such that $AK = LB \lt \frac{1}{2}AB$, $BM = NC \lt \frac{1}{2}BC$ and $CP = QA \lt \frac{1}{2}CA$. The intersections of $KN$ with $MQ$ and $LP$ are $R$ and $T$ respectively, and the intersections of $NP$ with $LM$ and $KQ$ are $D$ and $E$ respectively. Prove that the lines $DR$, $BE$ and $CT$ pass through a common point.