  We prove that the length of the projection of the vector joining the centers
of mass of a convex body on the plane and of its boundary to an arbitrary
direction does not exceed $\frac{1}{6}$ of the body width in this direction. It
follows that the distance between these centers of mass does not exceed
$\frac16$ of the diameter of the body and $\frac{1}{12}$ of its boundary
length. None of those constants can be improved.
