In triangle $ABC$, $\angle A =60^o$. Let $BB_1$ and $CC_1$ be angle bisectors of this triangle. Prove that the point symmetrical to vertex $A$ with respect to line $B_1C_1$ lies on side $BC$.
Source: Russian Regional Olympiad 2010 9.4
Tags: geometry, symmetry
In triangle $ABC$, $\angle A =60^o$. Let $BB_1$ and $CC_1$ be angle bisectors of this triangle. Prove that the point symmetrical to vertex $A$ with respect to line $B_1C_1$ lies on side $BC$.