1987 AIME Problems/Problem 2

Problem

What is the largest possible distance between two points, one on the sphere of radius 19 with center $(-2,-10,5)\displaystyle$ and the other on the sphere of radius 87 with center $\displaystyle (12,8,-16)$ ?

The distance between the two centers of the spheres can be determined via the distance formula in three dimensions: $\sqrt{(12 - (-2))^2 + (8 - (-10))^2 + (-16 - 5)^2} = \sqrt{14^2 + 18^2 + 21^2} = 31$ . The largest possible distance would be the sum of the two radii and the distance between the two centers, making it $19 + 87 + 31 = 137$ .