After studying the four-point * * * circle and proving △ ACD △ AEB, we can know that A, O, B, D, A, O, C and E have four-point * * * circles respectively.

Therefore, ∠ AOD = ∠ Abd = 60, ∠ AOE = ∠ AISI = 60.

That is, OA divides equally ∠DOE.