Question 139
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 in the same way. Let $G$ be the gravity center of the triangle $ABC$.
Prove that the points $A_1, B_1, C_1, G$ are concyclic.
Points $B_1$ and $C_1$ are defined in the same way. Let $G$ be the gravity center of the triangle $ABC$.
Prove that the points $A_1, B_1, C_1, G$ are concyclic.