MathNet 2020 — Math Olympiad Vault — Part 02 Question 149

A sphere is centered at a point with integer coordinates and passes through the three points $(2,0,0)$, $(0,4,0)$, $(0,0,6)$, but not the origin $(0,0,0)$. If $r$ is the smallest possible radius of the sphere, compute $r^{2}$.