1975 USAMO Problems/Problem 2

Problem

Let $A,B,C,D$ denote four points in space and $AB$ the distance between $A$ and $B$ , and so on. Show that

$AC^2+BD^2+AD^2+BC^2\ge AB^2+CD^2$ .

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1975 USAMO (Problems • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions