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.
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