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. O1, O2, O3, O4 are the circumcenters of
triangles AFG, AGE, BGF, and BGD, respectively. Prove that O1, O2, O3, O4
are concyclic.