The figure below shows a triangle ABC,
medians AD, BE, CF, and centroid G. O1, O2, O3, O4, O5, O6 are the circumcenters of
triangles AFG, AGE, BGF, BGD, CGD, CGE, respectively. Prove that O1, O2, O3, O4, O5, O6
are concyclic (lie on a same circle called van Lamoen circle).