MathDB
classical computational - triangle inscribed in triangle

Source: Romanian IMO TST 2005 - day 3, problem 2

April 19, 2005
geometryinradiusconicsinequalitiesperimeterincentergeometry proposed

Problem Statement

Let ABCABC be a triangle, and let DD, EE, FF be 3 points on the sides BCBC, CACA and ABAB respectively, such that the inradii of the triangles AEFAEF, BDFBDF and CDECDE are equal with half of the inradius of the triangle ABCABC. Prove that DD, EE, FF are the midpoints of the sides of the triangle ABCABC.