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, R_{1}, R_{2}, R_{3} are the circumradii of triangles
ABC, AHM, BDE, and CFG respectively, prove that
R = R_{1} + R_{2} + R_{3}.
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