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.
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