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GIH>90

Source: IMO ShortList 1990, Problem 5 (FRA 1)

May 31, 2005
geometryincentervectorEulertrigonometryorthocenterIMO Shortlist

Problem Statement

Given a triangle ABC ABC. Let G G, I I, H H be the centroid, the incenter and the orthocenter of triangle ABC ABC, respectively. Prove that ∠GIH>90∘ \angle GIH > 90^{\circ}.
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