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Parallelopiped and inequality

Source: Problem 5, Polish NO 1994

October 7, 2005
inequalitiesvectorLaTeXgeometryparallelogramtriangle inequalitygeometry solved

Problem Statement

A parallelopiped has vertices A1,A2,...,A8A_1, A_2, ... , A_8 and center OO. Show that: 4∑i=18OAi2≤(∑i=18OAi)2 4 \sum_{i=1}^8 OA_i ^2 \leq \left(\sum_{i=1}^8 OA_i \right) ^2
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