%0 Journal Article %T On a theorem of G. D. Chakerian %A Margarita Spirova %J Contributions to Discrete Mathematics %D 2010 %I University of Calgary %X Among all bodies of constant width in the Euclidean plane, a Reuleaux triangle of width $lambda$ has minimal area. But Reuleaux triangles are also minimal in another sense: if a convex body can be covered by a translate of any Reuleaux triangle, then it can be covered by a translate of any convex body of the same constant width. The first result is known as the Blaschke-Lebesgue theorem, and it is extended to an arbitrary normed plane in [19] and [5]. In the present paper we extend the second minimal property, known as Chakerian¡¯s theorem, to all normed planes. Some corollaries from this generalization are also given. %U http://cdm.math.ucalgary.ca/cdm/index.php/cdm/article/view/198