Let $A$ be the sum of all $10$ distinct products of the sides of a convex pentagon, $S$ be the area of the pentagon. a) Prove thas $S \le \frac15 A$. b) Does there exist a constant $c<\frac15$ such that $S \le cA$ ? I.Voronovich
Source: 2011 Belarus TST 4.1
Tags: geometry, pentagon, geometric inequality
Let $A$ be the sum of all $10$ distinct products of the sides of a convex pentagon, $S$ be the area of the pentagon. a) Prove thas $S \le \frac15 A$. b) Does there exist a constant $c<\frac15$ such that $S \le cA$ ? I.Voronovich