In the figure below, given a triangle ABC and the incircle O (inscribed circle), DE, FG, and HM are tangent to the incircle O and  parallel to AC, AB, and BC respectively. If P, P1, P2, P3 are the perimeters of triangles ABC, AHM, BDE, and CFG respectively, (1) prove that P = P1 + P2 + P3, and (2) DM = FG, DE = GH, EF = HM. Post your comments or solutions in the blog.