MathDB

Four Points in Space

Source: 1975 USAMO Problem 2

March 15, 2010

inequalitiesgeometryparallelogram

Problem Statement

Let

A,B,C,

and

D

denote four points in space and

AB

the distance between

A

and

B

, and so on. Show that AC^2\plus{}BD^2\plus{}AD^2\plus{}BC^2 \ge AB^2\plus{}CD^2.