Question 93
On the sides $AB$ and $AC$ of an acute triangle $ABC$ triangles $ABC_1$ and $AB_1C$ are constructed outside with $\angle BAC_1 = \angle B_1AC = 30^\circ$, $\angle AC_1B = \angle CB_1A = 60^\circ$. A point $A_1$ inside $ABC$ is such that $\angle CBA_1 = \angle BCA_1 = 30^\circ$. Prove that the points $A_1$, $B_1$ and $C_1$ are collinear.