The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean n-space E n is at most n +2. We obtain this estimate as an immediate consequence of our theorem which says that for an arbitrary convex body C in E n and for any simplex S of maximum volume contained in C the homothetical copy of S with ratio n + 2 and center in the barycenter of S contains C. In general, this ratio cannot be improved, as it follows from the example of any double-cone.Denote by C n the family of all convex bodies and by M n the family of all centrally symmetric convex bodies in Euclidean n-dimensional space E n .Finding simplices of large volume in convex bodies has a long history. See, for instance, the papers by Blaschke (1917) on the maximum area of triangles in planar convex bodies, by MacKinney McKinney (1974) on simplices of maximum volume in centrally symmetric convex bodies, and the survey article Hudelson et al. (1996) by Hudelson, Klee and Larman on simplices of large volume in cubes.Let A be an (n − 1)-dimensional convex body and let I = ab be a perpendicular to the hyperplane containing A non-degenerated segment centered at a point of A. We call the convex hull conv(A ∪ I ) the double pyramid with base A and apices a and b. If B is a ball of E n − 1 in place of A and if the centers of B and I coincide, the double-pyramid is called a double-cone.