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Problem 587: Triangle, Incenter, Incircle, Tangency Point, Midpoint, Distance, Half the Difference. Level: Mathematics Education, High School, College

The figure shows a triangle ABC (BC > AB). The incircle O is tangent to AC at D. If M is the midpoint of AC, prove that the measure of DM is equal to half the difference of BC and AB.
 

Triangle, Incircle, Tangency Point, Midpoint, Distance
 

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