Question Number 152697 by mathdanisur last updated on 31/Aug/21
$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\Sigma\:\frac{\left(\mathrm{r}_{\boldsymbol{\mathrm{a}}} +\mathrm{r}_{\boldsymbol{\mathrm{b}}} \right)\left(\mathrm{r}_{\boldsymbol{\mathrm{a}}} +\mathrm{r}_{\boldsymbol{\mathrm{c}}} \right)}{\mathrm{h}_{\boldsymbol{\mathrm{b}}} +\mathrm{h}_{\boldsymbol{\mathrm{c}}} }\:\geqslant\:\frac{\mathrm{9r}}{\mathrm{2}} \\ $$