Let n≥2, let A1,A2,…,An+1 be n+1 points in the
n-dimensional Euclidean space, not lying on the same hyperplane,
and let B be a point strictly inside the convex hull of
A1,A2,…,An+1. Prove that \angle A_iBA_j>90^\circ holds
for at least n pairs (i,j) with \displaystyle{1\le i<j\le
n+1}.Proposed by Géza Kós, Eötvös University, Budapest
college contestsgeometryvector geometryIMC2015