  In this paper, we study a reverse isoperimetric inequality for planar convex
bodies whose radius of curvature is between two positive numbers 0 < $\alpha$ <
$\beta$, called ($\alpha$, $\beta$)--convex bodies. We show that among planar
($\alpha$, $\beta$)--convex bodies of fixed perimeter, the extremal shape is a
domain whose boundary is composed by two arcs of circles of radius $\alpha$
joined by two arcs of circles of radius $\beta$.
