In $\Delta ABC$ the angles $ABC$ and $ACB$ are acute. Let $M$ be the midpoint of $AB$. Point $D$ is on the half-line $(CB$ such that $ B \in (CD)$ and $\angle DAB= \angle BCM$. Perpendicular from $B$ to line $CD$ intersects the line bisector of $AB$ in $E$. Prove that $DE$ and $AC$ are perpendicular.