Planet 9 From Outer Space

Geometry Level 5

8 points with integer coordinates are located on a \(8 \times 8\) lattice such that the sum of the squares of all 28 distances between each pair of them is 1216. There exists a locus of a \(9^\text{th}\) point such that the sum of the squares of all the distances between it and each of the 8 points on the lattice is 800. This locus is a circle. Find the radius of that circle.

Note: The graphic posted does not show actual locations of points or circle or radius.

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