The figure shows a triangle ABC with the orthocenter H and the centroid G. M is the midpoint of HG, AM = a, BM = b, CM = c, and R is the circumradius, Prove that a^{2} + b^{2} + c^{2} = 3.R^{2}.

Home | Search | Geometry | Problems | All Problems | Open Problems | Visual Index | Art | 741-750 | Triangles | Orthocenter | Centroid /Barycenter | Circumradius | Midpoints | Distances between Triangle Centers | Email | Solution / comment | by Antonio Gutierrez