Question 32
In a triangle $ABC$, the internal angle bisectors at vertices $B$ and $C$ intersect at point $I$ and intersect the sides $CA$ and $AB$ at points $E$ and $F$, respectively. Let $M$ and $N$ be the midpoints of segments $BI$ and $CI$, respectively. The line $FM$ intersects the external angle bisector at vertex $B$ of triangle $ABC$ at point $K$, and the line $EN$ intersects the external angle bisector at vertex $C$ of triangle $ABC$ at point $L$. Prove that the points $K, B, C$, and $L$ lie on the same circle.
