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Circumradius ineq PA/(AB*AC) + PB/(BC*BA) + PC/(CA*CB) > 1/R

Source: XIV Rioplatense Mathematical Olympiad (2005), Level 3

July 26, 2011
geometrycircumcircleinequalities unsolvedinequalities

Problem Statement

Let PP be a point inside triangle ABCABC and let RR denote the circumradius of triangle ABCABC. Prove that PAAB⋅AC+PBBC⋅BA+PCCA⋅CB≥1R. \frac{PA}{AB\cdot AC}+\frac{PB}{BC\cdot BA}+\frac{PC}{CA\cdot CB}\ge\frac{1}{R}.
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