Online Geometry Problem 846: Triangle, Medians, Centroid, Four Circumcenters,
Concyclic Points, Cyclic Quadrilateral, Similarity. Level: High School,
SAT Prep, College,
Mathematics Education

The figure below shows a triangle ABC,
medians AD, BE, CF, and centroid G. O_{1}, O_{2}, O_{3}, O_{4} are the circumcenters of
triangles AFG, AGE, BGF, and BGD, respectively. Prove that O_{1}, O_{2}, O_{3}, O_{4}
are concyclic.