In an acute triangle $ABC$ the angle bisector $AL$, $L \in BC$, intersects its circumcircle at $N$. Let $K$ and $M$ be the projections of $L$ onto sides $AB$ and $AC$. Prove that triangle $ABC$ and quadrilateral $A K N M$ have equal areas.
Problem
Source: 2011 Saudi Arabia BMO TST 1.3 - Balkan MO
Tags: areas, equal areas, geometry, circumcircle