\[\large a\sqrt{8}+b\sqrt{6}+c\sqrt{2}\geq k\sqrt{a^2+b^2+c^2}\]

Consider all possible side lengths \(a,b,c\) of a right triangle \(ABC\). What is the maximium value of \(k\) such that the inequality is always satisfied?

###### Cyprus TST pre IMO 2016.

Set.