MathNet 2005 — Part 03 Question 34

Let $ABCD$ be a parallelogram, $P$ a point on $CD$, and $Q$ a point on $AB$. Let also $M = AP \cap DQ$, $N = BP \cap CQ$, $K = MN \cap AD$, and $L = MN \cap BC$. Show that $BL = DK$.