In a scalene triangle ABC, H is the orthocenter, and G is the centroid. Let Ab and Ac be points on AB and AC, respectively, such that B, C, Ab, Ac are cyclic, and the points Ab, Ac, H are collinear. Oa is the circumcenter of the triangle AAbAc. Ob and Oc are defined similarly. Prove that the centroid of the triangle OaObOc lies on the line HG. geometryOlympiad GeometryComplex numbers geometryorthocenterCentroidevan orz