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Problem 590: Triangle, Incenter, Incircle, Tangency Point, Midpoint, Areas. 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 area of triangle ODM is equal to the sum of areas of triangles OEG and OFH.

Triangle, Incircle, Tangency Point, Midpoint, Perpendicular, Distance


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