Question 23
The angle at the vertex $B$ in a triangle $ABC$ is $120^\circ$. Let $A_1$, $B_1$ and $C_1$ be the points on the segments $\overline{BC}$, $\overline{CA}$ and $\overline{AB}$ respectively, such that $AA_1$, $BB_1$ and $CC_1$ are angle bisectors of the triangle $ABC$. Determine the angle $\angle A_1B_1C_1$. (Serbia 1997)