MathDB
Romania District Olympiad 2001 - Grade X

Source:

March 16, 2011
geometrycircumcirclegeometry proposed

Problem Statement

Consider an inscriptible polygon ABCDEABCDE. Let H1,H2,H3,H4,H5H_1,H_2,H_3,H_4,H_5 be the orthocenters of the triangles ABC,BCD,CDE,DEA,EABABC,BCD,CDE,DEA,EAB and let M1,M2,M3,M4,M5M_1,M_2,M_3,M_4,M_5 be the midpoints of DE,EA,AB,BCDE,EA,AB,BC and CDCD, respectively. Prove that the lines H1M1,H2M2,H3M3,H4M4,H5M5H_1M_1,H_2M_2,H_3M_3,H_4M_4,H_5M_5 have a common point.
Dinu Serbanescu
Back to ProblemsView on AoPS