A point $A_1$ is marked inside an acute non-isosceles triangle $ABC$ such that $\angle A_1AB = \angle A_1BC$ and $\angle A_1AC=\angle A_1CB$. Points $B_1$ and $C_1$ are defined same way. Let $G$ be the gravity center if the triangle $ABC$. Prove that the points $A_1,B_1,C_1,G$ are concyclic.