Online Geometry Problems

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.
 

Triangle, Medians, Centroid, Four Circumcenters, Concyclic Points, Cyclic Quadrilateral
 


 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 841-850 | Triangles | Centroid /Barycenter | Circumcenter | Cyclic Quadrilateral | Concyclic Points | Similarity | van Lamoen Circle | Email | Solution / comment | By Antonio Gutierrez