Some strengthened versions of Klamkin's inequality and applications
Euler's inequality for a \(n\)-dimesional simplex in \(n\)-dimensional Euclidean space is \[R\geq nr,\] where \(R\) and \(r\) are the circumradius and the inradius of the simplex, respectively. \textit{M. S. Klamkin} [Math. Modelling 6, 49--64 (1985; Zbl 0573.49012)] obtained the improvement \[R^2\geq n^2r^2 + |OI|^2,\] where \(O\) and \(I\) are the circumcenter and the incenter of the simplex. As the title indicates, the author gives two sharpenings of the last inequality, from which Euler's inequality follows as an easy corollary.
scientific article; zbMATH DE number 7367294