Position of the centroid of a planar convex body

Abstract

It is well known that any planar convex body A permits to inscribe an affine-regular hexagon \(H_A\). We prove that the centroid of A belongs to the homothetic image of \(H_A\) with ratio \(\frac{4}{21}\) and the center in the center of \(H_A\). This ratio cannot be decreased.