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Problem 592: Triangle, Incenter, Incircle, Tangency Point, Midpoints, Concurrent Lines, Congruence. Level: Mathematics Education, High School, College

The figure shows a triangle ABC with the incircle O tangent to AC at D. Points M, G, and H are the midpoints of AC, AB, and BC, respectively. Prove that lines GH, BD, and MO extended are concurrent at the same point E.
 

Triangle, Incircle, Incenter, Inradius, Midpoint, Altitude
 

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