Question 83
We are given $n$ ($n \ge 3$) points in the plane not all lying on the same line. For an arbitrary point $M$ we define $f(M)$ to be the sum of the distances from these $n$ points to $A$. It is known that there exists a point $M_1$ such that for every point $M$ of the plane the inequality $f(M_1) \le f(M)$ holds. Let $M_2$ be a point such that $f(M_1) = f(M_2)$. Prove that the points $M_1$ and $M_2$ coincide.