On the Circumradius of a Special Class of n-Simplices

An n -simplex is called circumscriptible (or edge-incentric) if there is a sphere which is tangent to all its n ( n + 1)/2 edges. We obtain a closed formula for the radius of the circumscribed sphere of a circumscriptible n -simplex, and we prove a double inequality involving the circumradius and the edge-inradius of such simplices. With these results a part of a problem posed by the authors is solved.