MathNet 1991 — Part 01 Question 65

$ABCD$ is a rectangle. Points $K$, $L$, $M$, $N$ are chosen on $AB$, $BC$, $CD$, $DA$ respectively so that $KL$ is parallel to $MN$, and $KM$ is perpendicular to $LN$. Show that the intersection of $KM$ and $LN$ lies on $BD$.