  We establish some relations between the perimeter, the area and the visual
angle of a planar compact convex set. Our first result states that Crofton's
formula is the unique universal formula relating the visual angle, length and
area. After that we give a characterization of convex sets of constant width by
means of the behaviour of its isotopic sets at infinity. Also for this class of
convex sets we prove that the existence of an isotopic circle is enough to
ensure that the considered set is a disc.
