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Angle inequality

Source: 239 2009 J7

July 29, 2020
inequalities

Problem Statement

In the triangle ABCABC, the cevians AA1AA_1, BB1BB_1 and CC1CC_1 intersect at the point OO. It turned out that AA1AA_1 is the bisector, and the point OO is closer to the straight line ABAB than to the straight lines A1C1A_1C_1 and B1A1B_1A_1. Prove that ∠BAC>120∘\angle{BAC} > 120^{\circ}.
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