MathDB

G2

Part of 2012 Balkan MO Shortlist

Problems(1)

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

9/25/2020
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
geometryorthocenterCircumcenter