Online Geometry Problems

Online Geometry Problem 841: Triangle, Medians, Centroid, 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. O1, O2, O3, O4, O5, O6, are the circumcenters of triangles AFG, AGE, BGF, BGD, CGD, and CGE, respectively. O1O2 cuts O4O3 at H. HM is perpendicular to O2O6 and HN is perpendicular to O4O5. Prove that (1) HM = BE/2, HN = AD/2; (2) HO4.HM = HO2.HN
 

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


 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 841-850 | Triangles | Centroid /Barycenter | Circumcenter | Perpendicular | Perpendicular Bisector | Congruence | Similarity | van Lamoen Circle | Email | Solution / comment | By Antonio Gutierrez