classical computational - triangle inscribed in triangle
Source: Romanian IMO TST 2005 - day 3, problem 2
April 19, 2005
geometryinradiusconicsinequalitiesperimeterincentergeometry proposed
Problem Statement
Let be a triangle, and let , , be 3 points on the sides , and respectively, such that the inradii of the triangles , and are equal with half of the inradius of the triangle . Prove that , , are the midpoints of the sides of the triangle .