  It is well-known since the time of the Greeks that two disjoint circles in
the plane have four common tangent lines. Cappell et al. proved a
generalization of this fact for properly separated strictly convex bodies in
higher dimensions. We have shown that the same generalization applies for
arbitrary convex bodies. When the number of convex sets involved is equal to
the dimension, we obtain an alternative combinatorial proof of Bisztriczky's
theorem on the number of common tangents to $d$ separated convex bodies in
$\Rr^d$.
