Question Number 171745 by Shrinava last updated on 20/Jun/22
$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\mathrm{triangle}\:\:\mathrm{ABC}\:, \\ $$$$\mathrm{with}\:\mathrm{area}\:\:\mathrm{F}\:\:\mathrm{holds}: \\ $$$$\mathrm{7}\left(\mathrm{m}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} \:+\:\mathrm{m}_{\boldsymbol{\mathrm{b}}} ^{\mathrm{2}} \:+\:\mathrm{m}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{2}} \right)\:\geqslant\:\mathrm{36F}\:+\:\mathrm{3}\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\left(\mathrm{a}−\mathrm{m}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} \right) \\ $$
Answered by floor(10²Eta[1]) last updated on 20/Jun/22
$$\mathrm{what}\:\mathrm{is}\:\mathrm{m}_{\mathrm{a}} ,\:\mathrm{m}_{\mathrm{b}} ,\:\mathrm{m}_{\mathrm{c}} ? \\ $$