Further improvement of the Klamkin inequality (Q2779014)

Let \({\mathcal A}\) be a simplex in the \(n\)-dimensional Euclidean space \(E^n\). Then the Klamkin inequality says that \(R^2\geq n^2r^2+ |OI |^2\) where \(R\) is the circumradius, \(r\) the inradius, \(O\) the circumcentre and \(I\) the incentre of \({\mathcal A}\); equality holds if and only if \({\mathcal A}\) is regular.NEWLINENEWLINENEWLINEIn this paper, the author sharpens and extends this inequality.