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abc(a+b+c)=3, show that prod(a+b)>=8 [Indian RMO 2012(b) Q4]

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December 2, 2012
inequalitiesgeometrycircumcircletrigonometrygeometric inequalityarea of a triangleHeron's formula

Problem Statement

Let a,b,ca,b,c be positive real numbers such that abc(a+b+c)=3.abc(a+b+c)=3. Prove that we have (a+b)(b+c)(c+a)≥8.(a+b)(b+c)(c+a)\geq 8. Also determine the case of equality.
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