Problem

Source: RMO 2024 Q3

Tags: geometry, circumcircle, trigonometry



Let ABC be an acute triangle with AB=AC. Let D be the point on BC such that AD is perpendicular to BC. Let O,H,G be the circumcenter, orthocenter and centroid of triangle ABC respectively. Suppose that 2OD=23HD. Prove that G lies on the incircle of triangle ABC.