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Let \(a,b,c\) be the sides of a triangle. Find the set of all possible values of \(\frac{a}{b + c} + \frac{b}{a + c} + \frac{c}{a + b}.\)

 Mar 8, 2019
edited by Guest  Mar 8, 2019
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\(\text{The expression seems to vary from }\dfrac 3 2\\ \text{which corresponds to an equilateral triangle to }2\\ \text{which corresponds to an isosceles triangle with one leg having zero length}\\ \dfrac 3 2 \leq \dfrac{a}{b+c}+ \dfrac{b}{a+c}+\dfrac{c}{a+b} < 2\)

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 Mar 8, 2019
edited by Rom  Mar 8, 2019

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