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six points in a plane, an inequality

Source: Yugoslav TST 1968 P1

May 29, 2021
inequalitiescombinatoricsgeometry

Problem Statement

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.
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