Question Number 183167 by Shrinava last updated on 21/Dec/22
$$\mathrm{In}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}: \\ $$$$\frac{\mathrm{m}_{\boldsymbol{\mathrm{b}}} }{\mathrm{b}}\:+\:\frac{\mathrm{m}_{\boldsymbol{\mathrm{c}}} }{\mathrm{c}}\:\leqslant\:\frac{\mathrm{a}}{\mathrm{2r}}\:\leqslant\:\frac{\mathrm{n}_{\boldsymbol{\mathrm{b}}} }{\mathrm{h}_{\boldsymbol{\mathrm{b}}} }\:+\:\frac{\mathrm{n}_{\boldsymbol{\mathrm{c}}} }{\mathrm{h}_{\boldsymbol{\mathrm{c}}} } \\ $$
Commented by mr W last updated on 22/Dec/22
$${i}\:{think}\:{not}\:{every}\:{body}\:{knows}\:{what}\:{is} \\ $$$${what}\:{in}\:{the}\:{equation}. \\ $$
Commented by Frix last updated on 22/Dec/22
$$\mathrm{That}'\mathrm{s}\:\mathrm{plain}\:\mathrm{to}\:\mathrm{see}\:\mathrm{because}\:\mathrm{obviously} \\ $$$$\left(\frac{\alpha}{\rho_{{b}} +\rho_{{c}} }+\frac{\beta}{\rho_{{a}} +\rho_{{c}} }\right)\left({i}_{{c}} −{j}_{{c}} \right)>\frac{\gamma}{\rho_{{a}} +\rho_{{b}} }\left(\left({i}_{{a}} −{j}_{{a}} \right)+\left({i}_{{b}} −{j}_{{b}} \right)\right) \\ $$