Online Geometry Problem 845: Triangle, Medians, Centroid, Four Circumcenters,
Perpendicular, Congruence, 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. O_{1}O_{2} cuts O_{4}O_{3}
at H. Prove
that HO_{3}.HO_{4} = HO_{1}.HO_{2}.