Question 58
The point $L$ is the internal point of the side $AC$ of the isosceles triangle $ABC$ ($AB = BC$). The circle $\omega$ goes through $B$ and is tangent to $AC$ at $L$. It intersects the line $AB$ at points $B$ and $D$ and the line $BC$ at points $B$ and $E$. Let $M$ be the midpoint of the segment $DE$ and let $N \neq L$ be the intersection of the lines $BM$ and $AC$. Given that $\frac{AN}{CN} = \frac{AL}{CL} \gt 1$ prove that the angle $ALB$ equals $60^\circ$.