Problem

Source: III International Festival of Young Mathematicians Sozopol 2012, Theme for 10-12 grade

Tags: geometry, angle bisector



In a non-isosceles $\Delta ABC$ with angle bisectors $AL_a$, $BL_b$, and $CL_c$ we have that $L_aL_c=L_bL_c$. Prove that $\angle C$ is smaller than $120^\circ$.