, 2011

Let $ABC$ be a triangle with $\angle CAB$ a right-angle. The point $L$ lies on the side $BC$ between $B$ and $C$. The circle $ABL$ meets the line $AC$ again at $M$ and the circle $CAL$ meets the line $AB$ again at $N$. Prove that $L$, $M$ and $N$ lie on a straight line.