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Geometric inequalities involving the stretch of a set

A number of papers have been written concerning the properties of triangles which circumscribe convex sets, see for example (1), (2), (3). In this note we shall characterise two set functionals, one of which has already been introduced in (6). This will enable us to produce some new results in the spirit of those obtained in the papers mentioned above. These two functionals are interesting in that although they are defined in a rather abstruse manner, they turn out to have an intuitive geometric meaning, namely that they are the minimal widths of certain circumscribing triangles.