278. Let $a, b, c$ be the lengths of the sides of triangle $ABC$, and $M$ be an arbitrary point on the plane. Find the minimum of the expression

$$
|M A|^{2}+|M B|^{2}+|M C|^{2}
$$
278. The minimum is $\frac{a^{2}+b^{2}+c^{2}}{3}$ and is achieved if $M-$ is the centroid of $\triangle A B C$. (This can be proven, for example, using the coordinate method or by using Leibniz's theorem - see problem 153.)