Concyclic Points from Reflections of the Circumcenter about the Altitudes
Let ABC be a triangle with circumcenter O. Let A'', B'', and C'' be the reflections of O in the altitudes AA', BB', and CC', respectively. Then A'', B'', C'', and O are concyclic.
See figure 3 in Two Triads of Congruent Circles from Reflections.