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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.