51. At the base of a triangular pyramid lies a triangle with sides $a, b$ and $c$, the opposite lateral edges of the pyramid are equal to $m, n$ and $p$ respectively. Find the distance from the vertex of the pyramid to the centroid of the base.
51. $\frac{1}{3} \sqrt{3 m^{2}+3 n^{2}+3 p^{2}-a^{2}-b^{2}-c^{2}}$.