2. Find the maximum distance between two points, one on the surface of a sphere centered at $(-2$, $-10,5)$ with a radius of 19, and the other on the surface of a sphere centered at $(12,8,-16)$ with a radius of 87.
2. Let $O$ and $O_{1}$ be the centers of two spheres, and $P, P_{1}$ be the intersection points of the extended line segment $O_{1}$ with the two spherical surfaces, such that $O$ is inside $P O_{1}$ and $O_{1}$ is inside $O P_{1}$. Clearly, the maximum distance between these two points is $P P_{1}=P O+O O_{1}+O_{1} P_{1}=19+31+87=137$.
(Where $\left.O O_{1}=\sqrt{ }[12-(-2)] 2+[8-(-10)] 21\right)-(16-5)^{2}=\sqrt{961}=31$ ).