Abstract
A generalization and the dual version of the following result due to Firey is given: The mixed area of a plane convex body and its polar dual is at least $\pi$. We give a sharp upper bound for the product of the dual cross-sectional measure of any index and that of its polar dual. A general result for a convex body $K$ and a convex increasing real-valued function gives inequalities for sets of constant width and sets with equichordal points as special cases.
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