AUSTRIAN-POLISH 1986 Problem 1

A non-right triangle $A_1A_2A_3$ is given. Circles $C_1$ and $C_2$ are tangent at $A_3, C_2$ and $C_3$ are tangent at $A_1$ , and $C_3$ and $C_1$ are tangent at $A_2$ . Points $O_1,O_2,O_3$ are the centers of $C_1, C_2, C_3$ , respectively. Supposing that the triangles $A_1A_2A_3$ and $O_1O_2O_3$ are similar, determine their angles.