Let $E$ be an euclidean vector space and let $x_1,\ldots,x_n$ be vectors in $E$, such that :
$$\forall(i,j)\in \left\{1,\ldots,n\right\}^2,i\neq j\Rightarrow\Vert x_i-x_j\Vert\ge2$$
I want to show that there exists at least an index $i\in \{1,\ldots,n\}$ such that :
$$\Vert x_i\Vert\ge\sqrt{\frac{2(n-1)}{n}}$$
Any hint would be appreciated.