On a certain triangle transformation and some of its applications (Q750898)

From a triangle with side lengths a, b, c, area F, and radii R, r of circumscribed and inscribed circles the authors construct another with parameters \(a'\), \(b'\), \(c'\), \(F'\), \(R'\) and \(r'\), depending on a real parameter \(k>1\). They apply this construction to obtain a lot of inequalities between the above parameters. They refer to a book of \textit{O. Bottema} and others on `Geometric Inequalities', Noordhoff (1969; Zbl 0174.524) and to a longer paper in Russian.