MathDB

A1

Part of 1964 Putnam

Problems(1)

six points in a plane, an inequality

Source: Yugoslav TST 1968 P1

5/29/2021
Given 66 points in a plane, assume that each two of them are connected by a segment. Let DD be the length of the longest, and dd the length of the shortest of these segments. Prove that Dd≥3\frac Dd\ge\sqrt3.
inequalitiescombinatoricsgeometry