MathDB
Geometry Inequality

Source: Vietnam NMO 1986 Problem 2

February 6, 2009
geometryinequalitiescircumcircleinradiustrigonometry3D geometrypyramid

Problem Statement

Let R R, r r be respectively the circumradius and inradius of a regular 1986 1986-gonal pyramid. Prove that \frac{R}{r}\ge 1\plus{}\frac{1}{\cos\frac{\pi}{1986}} and find the total area of the surface of the pyramid when the equality occurs.
Back to ProblemsView on AoPS