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< ABC <= 180^o/ m

Source: Switzerland - 2004 Swiss MO Final Round p7

December 26, 2022
combinatoricscombinatorial geometry

Problem Statement

Given are m≥3m\ge 3 points in the plane. Prove that you can always choose three of these points A,B,CA,B,C such that ∠ABC≤180om.\angle ABC \le \frac{180^o}{m}.
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