Online Geometry Problems

Online Geometry Problem 843: Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Parallel, Congruence, 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. O1O2 cuts O4O3 at H. CP is parallel to AD (P on BE extended). Prove that HO3.CP = HO1.GP.

Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Parallel, Congruence, Similarity


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