MathNet 2015-part-01 — 191 problems (EN–VI) Question 181

The hexagon $ABLCDK$ is inscribed and the line $LK$ intersects the segments $AD$, $BC$, $AC$ and $BD$ in points $M$, $N$, $P$ and $Q$, respectively. Prove that $NL \cdot KP \cdot MQ = KM \cdot PN \cdot LQ$.