Question Number 176727 by Shrinava last updated on 25/Sep/22
$$\mathrm{In}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}: \\ $$$$\mathrm{6r}\:\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{r}_{\boldsymbol{\mathrm{a}}} }{\mathrm{s}\:+\:\mathrm{n}_{\boldsymbol{\mathrm{a}}} }\:\:+\:\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\mathrm{n}_{\boldsymbol{\mathrm{a}}} \:\geqslant\:\mathrm{3s} \\ $$