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CG with convex polygon inside a square and weak bound

Source: Moldova TST 2024 P5

June 9, 2024
combinatorial geometry

Problem Statement

Consider a natural number n≥3n \ge 3. A convex polygon with nn sides is entirely placed inside a square with side length 1. Prove that we can always find three vertices of this polygon, the triangle formed by which has area not greater than 8n2\frac{8}{n^2}.
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