An isoperimetric theorem in plane geometry (Q1404502)

The author proves a general covering theorem for simple polygons in the plane, from which he deduces, besides some new inequalities of isoperimetric type, the following known corollary. Let \(F\) be a polygon. Then among all polygons with edges congruent to those of \(F\), those polygons whose vertices lie on a circle have the greatest area. The new approach is interesting since it does not need any previous isoperimetric inequality; thus it gives a satisfactory response to a remark made by \textit{I. M. Yaglom} and \textit{V. G. Boltyanskii} in their book [`Convex fiqures' (Library of the Mathematical Circle, New York) (1961; Zbl 0098.35501)].