Question 75
Let $A_0A_1A_2$ be a triangle and let $O$ be its circumcenter. The lines $OA_k$ and $A_{k+1}A_{k+2}$ meet at $B_k$, and the tangent of the circumcircle $A_0A_1A_2$ at $A_k$ meets the line $B_{k+1}B_{k+2}$ at $C_k$, $k = 0, 1, 2$, indices being reduced modulo $3$. Show that the points $C_0, C_1, C_2$ are collinear.