# Problem 42

Algebra Level 5

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

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?

Set.

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