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.