Let O be the circumcenter; Oa, Ob, Oc the circumcenters of OBC, OCA, OAB. Let Oab, Oac be the  isogonals of Oa in OAC, OAB. Define analogously Obc, Oba, Oca, Ocb. The six points Oab, Oac, Obc, Oba, Oca, Ocb lie in a conic.