Question 145
Points $B_1$ and $C_1$ are marked respectively on the sides $AB$ and $AC$ of an acute isosceles triangle $ABC$ ($AB = AC$) such that $BB_1 = AC_1$. The points $B$, $C$, and $S$ lie in the same half-plane with respect to the line $B_1C_1$ so that
$$
\angle SB_1C_1 = \angle SC_1B_1 = \angle BAC.
$$
Prove that $B$, $C$, $S$ are collinear if and only if the triangle $ABC$ is equilateral.
$$
\angle SB_1C_1 = \angle SC_1B_1 = \angle BAC.
$$
Prove that $B$, $C$, $S$ are collinear if and only if the triangle $ABC$ is equilateral.