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best constant C such that S/(ab+bc+ca)<= C

Source: 2017 Swedish Mathematical Competition p5

May 1, 2021

algebrainequalitiesGeometric Inequalities

Problem Statement

Find a costant

C

, such that

\frac{S}{ab+bc+ca}\le C

where

a,b,c

are the side lengths of an arbitrary triangle, and

S

is the area of the triangle. (The maximal number of points is given for the best possible constant, with proof.)