Sums

[Zan]

$n\geq4\in\mathbb{N}$. Prove that from any set of non-negative real numbers $x_1,\ldots,x_n$ with $x_1+\ldots+x_n\leq200$ and $x_1^2+\ldots+x_n^2\geq2500$, four numbers with sum at least 50 can be chosen.