Online Geometry Problems

Online Geometry Problem 847: van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters, Concyclic Points. 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, O5, O6 are the circumcenters of triangles AFG, AGE, BGF, BGD, CGD, CGE, respectively. Prove that O1, O2, O3, O4, O5, O6 are concyclic (lie on a same circle called van Lamoen circle).
 

van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters, Concyclic Points
 


 

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