  Let $C$ be a convex body and let $S$ be a nondegenerate simplex in ${\mathbb
R}^n$. Denote by $\xi(C;S)$ the minimal $\tau>0$ such that $C$ is a subset of
the simplex $\tau S$. By $\alpha(C;S)$ we mean the minimal $\tau>0$ such that
$C$ is contained in a translate of $\tau S$. Earlier the author has proved the
equalities $\xi(C;S)=(n+1)\max\limits_{1\leq j\leq n+1} \max\limits_{x\in
C}(-\lambda_j(x))+1$ \ (if $C\not\subset S$), \ $\alpha(C;S)=
\sum\limits_{j=1}^{n+1} \max\limits_{x\in C} (-\lambda_j(x))+1.$ Here
$\lambda_j$ are linear functions called the basic Lagrange polynomials
corresponding to $S$. In his previous papers, the author has investigated these
formulae if $C=[0,1]^n$. The present paper is related to the case when $C$
coincides with the unit Euclidean ball $B_n=\{x: \|x\|\leq 1\},$ where
$\|x\|=\left(\sum\limits_{i=1}^n x_i^2 \right)^{1/2}.$ We establish various
relations for $\xi(B_n;S)$ and $\alpha(B_n;S)$, as well as we give their
geometric interpretation.
