In-ABC-holds-1-6r-h-a-h-b-h-b-h-c-h-c-h-a-1-3-3R-

Question Number 227954 by hardmath last updated on 04/Mar/26

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{holds}: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{6r}\:\leqslant\:\sqrt[{\mathrm{3}}]{\left(\mathrm{h}_{\boldsymbol{\mathrm{a}}} \:+\:\mathrm{h}_{\boldsymbol{\mathrm{b}}} \right)\centerdot\left(\mathrm{h}_{\boldsymbol{\mathrm{b}}} \:+\:\mathrm{h}_{\boldsymbol{\mathrm{c}}} \right)\centerdot\left(\mathrm{h}_{\boldsymbol{\mathrm{c}}} +\:\mathrm{h}_{\boldsymbol{\mathrm{a}}} \right)}\:\leqslant\:\mathrm{3R} \\ $$

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