The figure below shows a triangle ABC,
medians AD, BE, CF, and centroid G. O_{1}, O_{2}, O_{3}, O_{4}, O_{5}, O_{6} are the circumcenters of
triangles AFG, AGE, BGF, BGD, CGD, CGE, respectively. Prove that O_{1}, O_{2}, O_{3}, O_{4}, O_{5}, O_{6}
are concyclic (lie on a same circle called van Lamoen circle).
