Optimizing area and perimeter of convex sets for fixed circumradius and inradius
The authors determine the planar convex sets with fixed values of their circumradius and inradius that either maximize or minimize the area (also the perimeter). The corresponding geometric inequalities are explicitly obtained. Using these new inequalities jointly with the classical inequalities concerning these geometric magnitudes, the authors build complete systems of inequalities for the cases \((A,R,r)\) and \((p,R,r)\); these problems were posed by Santaló in 1961.
scientific article; zbMATH DE number 1903790