MathDB
inradii

Source: Russian 2007

August 28, 2007
geometrygeometric transformationhomothetygeometry proposed

Problem Statement

A point D D is chosen on side BC BC of a triangle ABC ABC such that the inradii of triangles ABD ABD and ACD ACD are equal. Consider in these triangles the excircles touching sides BD BD and CD CD, respectively. Prove that their radii are also equal.