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If-x-y-z-gt-0-then-in-ABC-holds-yz-h-a-2-R-2-4F-2-x-y-z-2-




Question Number 205203 by hardmath last updated on 12/Mar/24
If   x,y,z>0   then in   △ABC   holds:  Σ  ((yz)/h_a ^2 )  ≤  (R^2 /(4F^2 ))  (x + y + z)^2
$$\mathrm{If}\:\:\:\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{in}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\Sigma\:\:\frac{\mathrm{yz}}{\mathrm{h}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} }\:\:\leqslant\:\:\frac{\mathrm{R}^{\mathrm{2}} }{\mathrm{4F}^{\mathrm{2}} }\:\:\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)^{\mathrm{2}} \\ $$

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