Online Geometry Problem 845: Triangle, Medians, Centroid, Four Circumcenters,
Perpendicular, Congruence, Similarity. Level: High School,
SAT Prep, College,
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. O1O2 cuts O4O3
at H. Prove
that HO3.HO4 = HO1.HO2.