In the figure below, given a triangle ABC and the incircle of center I (inscribed circle), DE, FG, and HM are tangent to the incircle I and  parallel to AC, AB, and BC respectively. If r, r1, r2, r3 are the inradii of triangles ABC, AHM, BDE, and CFG respectively, prove that
r = r1 + r2 + r3. Post your comments or solutions in the blog.