I am looking for a proof of the problem as following:
Let $A_1, A_2, A_3, A_4, A_5, A_6$ lie on a circle. Let $A_{i-1}A_i$ meets $A_{i+1}A_{i+2}$ at $B_i$. We take modulo 6. Let $O_i$ be the center of circle $(B_{i-1}A_iB_{i+1})$. Let $O_1O_4$ meets $B_1B_4$ at $M$, $O_2O_5$ meets $B_2B_5$ at $N$, $O_3O_6$ meets $B_3B_6$ at $P$. Then show that three points $M, N, P$ are collinear.
