Question 17
In an acute triangle $ABC$ the inner bisector of the angle $A$ cuts to $BC$ at $L$ and cuts the circumscribed circumference of $ABC$ again on $N$. We draw perpendiculars from $L$ to $AB$ and $AC$, with feet $K$ and $M$, respectively. Prove that the quadrilateral $AKNM$ and triangle $ABC$ have the same area.