KöMaL 2014 B4598

The diagonals of a cyclic quadrilateral ABCD intersect at $E$, the midpoints of sides $AB$ and $CD$ are $K$ and $M$, and the perpendicular projections of point $E$on the sides $BC$ and $AD$ are $L$ and $N$, respectively. Prove that the lines $KM$and $LN$ are perpendicular to each other.