An estimate of the centroid Banach-Mazur distance between planar convex bodies

We consider the variant of the Banach-Mazur distance ${\delta }_{BM}^{\mathrm{c}\mathrm{e}\mathrm{n}}(C,D)$ of two convex bodies $C,D$ of $E^d$ with the additional requirement that the centroids of them coincide. We prove that ${\delta }_{BM}^{\mathrm{c}\mathrm{e}\mathrm{n}}(C,D)\le \frac{69}{17}$ for every $C,D$ of $E^2$.