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Problem 588: Triangle, Incenter, Incircle, Tangency Point, Midpoint, Distance, Sum. Level: Mathematics Education, High School, College

The figure shows a triangle ABC (BC > AC > AB). The incircle O is tangent to AC, AB, and BC at D, E, and F, respectively. If M, G, and H are the midpoints of AC, AB, and BC, respectively, prove that the measure of DM is equal to the sum of EG and FH.

Triangle, Incircle, Tangency Points, Midpoints

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