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Isosceles triangle and right angle

Source: Romanian District Olympiad 2006, Grade 7, Problem 4

March 11, 2006
vector

Problem Statement

Let ABCABC be a triangle with AB=ACAB=AC. Let DD be the midpoint of BCBC, MM the midpoint of ADAD and NN the foot of the perpendicular from DD to BMBM. Prove that ∠ANC=90∘\angle ANC = 90^\circ.
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