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Geometry Inequality

Source: 1985 National High School Mathematics League, Exam Two, Problem 4

February 24, 2020
geometryinequalities

Problem Statement

Given 5 points on a plane. Let λ\lambda be the ratio of maximum value between the points to minimum value between the points. Prove that λ≥2sin⁡310π\lambda\geq2\sin\frac{3}{10}\pi.
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