Consider the triangle formed by joining the circumcenter, the incenter and the centroid of a triangle (is there is already a name for this triangle in literature?). Simulations show that the line joining the incenter and the circumcenter always subtends and obtuse angle at centroid (except when the triangle is degenerate).
Conjecture: In any triangle, the line joining the incenter and the circumcenter always subtends and obtuse angle at centroid.
Can this be proved or disproved?