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right angle between centroid, circumenter and Nagel iff <A=60

Source: Sharygin Geometry Olympiad 2016 First Round P15 grades 9-11

July 25, 2018
geometryNagel pointright anglecircumcircle

Problem Statement

Let O,M,NO, M, N be the circumcenter, the centroid and the Nagel point of a triangle. Prove that angle MONMON is right if and only if one of the triangle’s angles is equal to 60o60^o.
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