CN-SMO 2007 Problem 6

In right-angle triangle $ABC$ , $\angle C=90$ °, Point $D$ is the midpoint of side $AB$ . Points $M$ and $C$ lie on the same side of $AB$ such that $MB\bot AB$ , line $MD$ intersects side $AC$ at $N$ , line $MC$ intersects side $AB$ at $E$ . Show that $\angle DBN=\angle BCE$ .