Question Number 22079 by Tinkutara last updated on 10/Oct/17
$$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{and}\:{h}_{{a}} \:\mathrm{the} \\ $$$$\mathrm{altitude}\:\mathrm{through}\:{A}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\left({b}\:+\:{c}\right)^{\mathrm{2}} \:\geqslant\:{a}^{\mathrm{2}} \:+\:\mathrm{4}{h}_{{a}} ^{\mathrm{2}} . \\ $$$$\left(\mathrm{As}\:\mathrm{usual}\:{a},\:{b},\:{c}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sides}\:{BC},\right. \\ $$$$\left.{CA},\:{AB}\:\mathrm{respectively}.\right) \\ $$
Commented by ajfour last updated on 11/Oct/17
$${solved}.\:{See}\:{Q}.\mathrm{22116} \\ $$