On a problem of P. Erdös
\textit{P. Erdös} has proposed the following minimal problem [J. Math. Phys. High School Students (1993)]: For an arbitrary triangle \(T\) (in the Euclidean plane) and arbitrary point \(X\), let \(a\), \(b\), \(c\) and \(x\), \(y\), \(z\) denote the distances of \(X\) from vertices and sides of \(T\), respectively. When does the ratio \({a + b + c \over x + y + z}\) have the minimum value? In this note are given results about the existence and uniqueness of solutions. This Erdös problem is related to the Fermat problem and a fractional programming.
scientific article; zbMATH DE number 897404