MathDB

Problem 5

Part of 1970 Bulgaria National Olympiad

Problems(1)

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

Source: Bulgaria 1970 P5

6/22/2021
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.
inequalitiesGeometric Inequalitiesgeometrypolygon