Hello, SyNtHeSiS!

Code:

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Construct a line through and the center of the sphere

It will intersect the sphere in two points, and

. . We want , the point further from

The line from to has direction

The line has parametric equations: .

Substitute into the equation of the sphere:

. .

. .

. .

I suspect that point is further from , but let's make sure.

Distance from to

. .

Distance from to

. .

Hence, is the point we are seeking.

Therefore: .