Question 21
(USS 4) (IMO2) The prolongation of the bisector $AL$ ($L\in BC$) in the acute-angled triangle $ABC$ intersects the circumscribed circle at point $N$. From point $L$ to the sides $AB$ and $AC$ are drawn the perpendiculars $LK$ and $LM$ respectively. Prove that the area of the triangle $ABC$ is equal to the area of the quadrilateral $AKNM$.