BALKAN-SL 2013 G5

Let $ABC$ be an acute triangle with $AB < AC < BC$ inscribed in a circle $(c)$ and let $E$ be an arbitrary point on its altitude $CD$ . The circle $(c_1)$ with diameter $EC$ , intersects the circle $(c)$ at point $K$ (different than $C$ ), the line $AC$ at point $L$ and the line $BC$ at point $M$ . Finally the line $KE$ intersects $AB$ at point $N$ . Prove that the quadrilateral $DLMN$ is cyclic.