Isoperimetric characterization of the incenter of a triangle (Q372495)

The author gives an isoperimetric characterization of the incenter of a triangle. He defines a cone isoperimetric center of a compact set of height \(h\). He demonstrates the next two theorems:NEWLINENEWLINE 1) In a triangle \(ABC\) exists a cone isoperimetric center of height h for any \(h>0\);NEWLINENEWLINE 2) The cone isoperimetric center of height h coincides with the incenter for any \(h>0\). The height of the isoperimetrically optimal cone is \(2^{3/2}\) times the radius of the inscribed circle.