Question Number 102705 by dw last updated on 10/Jul/20
$${For}\:{what}\:{values}\:{of}\:{k}\:\left({cosA}−\frac{\mathrm{1}}{\mathrm{5}}\right)\left({cosB}−\frac{\mathrm{1}}{\mathrm{5}}\right)\left({cosC}−\frac{\mathrm{1}}{\mathrm{5}}\right)\leqslant{k} \\ $$$${hold}\:{in}\:{all}\:{triangles}\:{ABC}? \\ $$