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In-ABC-prove-that-r-a-r-b-r-a-r-c-h-b-h-c-9r-2-




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

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