Analytical Solution for the Generalized Fermat-Torricelli Problem

We present explicit analytical solution for the problem of minimization of the function $F(x,y)= \sum_{j=1}^3 m_j \sqrt{(x-x_j)^2+(y-y_j)^2}$, i.e. we find the coordinates of stationary point and the corresponding critical value of $F(x,y)$ as functions of ${m_j,x_j,y_j}_{j=1}^3$. In addition, we also discuss inverse problem of finding such values of $m_1,m_2,m_3$ with the aim for the corresponding function $F$ to posses a prescribed position of stationary point.