Inscribed simplexes of a convex body

This paper advances the theorem that for any smooth point M of the boundary of a convex body K Rⁿ there exists a nondegenerate simplex inscribed in K with a vertex at M that is similar to a given n-dimensional simplex. Similar problems are considered and unanswered questions are posed.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 47–49, 1992.