KöMaL 2016 A667

On the circumcircle of the scalene triangle $ABC$ , let $A_0$, $B_0$, and $C_0$ be the midpoints of the arcs $BAC$ , $CBA$ and $ACB$ , respectively. Denote by $A_1$, $B_1$ and $C_1$ the Feuerbach points of the triangles $AB_0C_0$, $BC_0A_0$ and $CA_0B_0$, respectively. Show that the triangles $A_0B_0C_0$ and $A_1B_1C_1$ are similar.