In a triangle $ABC, L$ and $K$ are the points of intersections of the angle bisectors of $\angle ABC$ and $\angle BAC$ with the segments $AC$ and $BC$, respectively. The segment $KL$ is angle bisector of $\angle AKC$, determine $\angle BAC$.
Source: Training for IMO/Cono sur
Tags: geometry, angle bisector
In a triangle $ABC, L$ and $K$ are the points of intersections of the angle bisectors of $\angle ABC$ and $\angle BAC$ with the segments $AC$ and $BC$, respectively. The segment $KL$ is angle bisector of $\angle AKC$, determine $\angle BAC$.