In triangle $ ABC$, points $ M,N$ lie on line $ AC$ such that $ MA=AB$ and $ NB=NC$. Also $ K,L$ lie on line $ BC$ such that $ KA=KB$ and $ LA=LC$. It is know that $ KL=\frac12{BC}$ and $ MN=AC$. Find angles of triangle $ ABC$.
Source: Iranian National Olympiad (3rd Round) 2004
Tags: geometry proposed, geometry
In triangle $ ABC$, points $ M,N$ lie on line $ AC$ such that $ MA=AB$ and $ NB=NC$. Also $ K,L$ lie on line $ BC$ such that $ KA=KB$ and $ LA=LC$. It is know that $ KL=\frac12{BC}$ and $ MN=AC$. Find angles of triangle $ ABC$.