ELMO SL 2012 A10

Let $A_1A_2A_3A_4A_5A_6A_7A_8$ be a cyclic octagon. Let $B_i$ by the intersection of $A_iA_{i+1}$ and $A_{i+3}A_{i+4}$ . (Take $A_9 = A_1$ , $A_{10} = A_2$ , etc.) Prove that $B_1, B_2, \ldots , B_8$ lie on a conic.

David Yang.