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A regular 14-gon with side a is inscribed in a circle

Source: IMO LongList 1988, Vietnam 3, Problem 91 of ILL

November 9, 2005
trigonometrygeometry unsolvedgeometry

Problem Statement

A regular 14-gon with side aa is inscribed in a circle of radius one. Prove 2−a2⋅a>3⋅cos⁡(π7). \frac{2-a}{2 \cdot a} > \sqrt{3 \cdot \cos \left( \frac{\pi}{7} \right)}.
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