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line passes through orthocenter iff AB=AC or <BCA=120^o, circumcenter related

Source: 2012 Italy TST 2.1 - also 2012 Balkan Shortlist G2 BMO

September 25, 2020
geometryorthocenterCircumcenter

Problem Statement

Let ABCABC be a triangle, and let ℓ\ell be the line passing through the circumcenter of ABCABC and parallel to the bisector of the angle ∠A\angle A. Prove that the line ℓ\ell passes through the orthocenter of ABCABC if and only if AB=ACAB = AC or ∠BAC=120o\angle BAC = 120^o
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