MathDB
IMC2015, problem 5

Source: IMC2015

July 29, 2015
college contestsgeometryvector geometryIMC2015

Problem Statement

Let n≥2n\ge2, let A1,A2,…,An+1A_1,A_2,\ldots,A_{n+1} be n+1n+1 points in the nn-dimensional Euclidean space, not lying on the same hyperplane, and let BB be a point strictly inside the convex hull of A1,A2,…,An+1A_1,A_2,\ldots,A_{n+1}. Prove that \angle A_iBA_j>90^\circ holds for at least nn pairs (i,j)(i,j) with \displaystyle{1\le i<j\le n+1}.
Proposed by Géza Kós, Eötvös University, Budapest
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