Problem

Source: Tuymaada Junior 2007 p4

Tags: geometry, circumcircle, orthocenter, incenter, Circumcenter, angles



An acute-angle non-isosceles triangle $ ABC $ is given. The point $ H $ is its orthocenter, the points $ O $ and $ I $ are the centers of its circumscribed and inscribed circles, respectively. The circumcircle of the triangle $ OIH $ passes through the vertex $ A $. Prove that one of the angles of the triangle is $ 60^\circ $.