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side length of inscribable n-gon, inequality with circumscribed n+1-gon

Source: Bulgaria 1970 P5

June 22, 2021
inequalitiesGeometric Inequalitiesgeometrypolygon

Problem Statement

Prove that for n≥5n\ge5 the side of regular inscribable nn-gon is bigger than the side of regular n+1n+1-gon circumscribed around the same circle and if n≤4n\le4 the opposite statement is true.
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