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China Northern Mathematical Olympiad 2017, Problem 5

Source: China Northern Mathematical Olympiad 2017

July 29, 2017
geometrySpiral Similaritycircumcircle

Problem Statement

Triangle ABCABC has AB>ACAB > AC and ∠A=60∘\angle A = 60^\circ . Let MM be the midpoint of BCBC, NN be the point on segment ABAB such that ∠BNM=30∘\angle BNM = 30^\circ. Let D,ED,E be points on AB,ACAB, AC respectively. Let F,G,HF, G, H be the midpoints of BE,CD,DEBE, CD, DE respectively. Let OO be the circumcenter of triangle FGHFGH. Prove that OO lies on line MNMN.
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