  Often some interesting or simply curious points are left out when developing
a theory. It seems that one of them is the existence of an upper bound for the
fraction of area of a convex and closed plane area lying outside a circle with
which it shares a diameter, a problem stemming from the theory of isoperimetric
inequalities. In this paper such a bound is constructed and shown to be
attained for a particular area. It is also shown that convexity is a necessary
condition in order to avoid the whole area lying outside the circle.
