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AI || OH iff BAC = 120 degrees

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September 1, 2010
geometryincentercircumcircleCentroidIMO ShortlistIMO Longlist

Problem Statement

Let I,H,OI,H,O be the incenter, centroid, and circumcenter of the nonisosceles triangle ABCABC. Prove that AI∥HOAI \parallel HO if and only if ∠BAC=120∘\angle BAC =120^{\circ}.
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