Problem 3 of the Balkan Mathematical Olympiad 2014

Let ABCD be a trapezium inscribed in a circle \Gamma with diameter AB. Let E be the intersection point of the diagonals AC and BD. The circle with center B and radius BE meets \Gamma at the points K and L, where K is on the same side of AB as C. The line perpendicular to BD at E intersects CD at M.

Prove that KM is perpendicular to DL.

I placed two solutions on a separate page