[CFrame stuff] Get sphere center from rotation, radius and surface point

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I have a Part that is placed over an imaginary Sphere’s surface. Not really the Spherical coordinates system though. Anyway, my issue goes:
Given I have this data:

  • center: Vector3, the center point of a sphere,
  • rotation: CFrame, the rotation matrix relative to the angle 0,
  • radius: number, needn’t explain,

I can calculate the position of the Part (surface point) using the formula

part.CFrame = CFrame.new(center) * rotation * CFrame.new(Vector3.new(0, radius, 0))

Okay, this works. Now the problem.
Knowing the rotation matrix, radius and the part’s position, I want to calculate the actual center point of the sphere. I’ve tried this:

CFrame.new(Part.Position) * CFrame.Angles(rotation):Inverse() * CFrame.new(Vector3.new(0, -radius, 0)))
-- rotation is simply the actual rotation, since i dont need to invert the whole cframe

This works, partially. So what happens is, in literally every case, the X axis is substracted by 10.383215, and the Z axis is added by that exact number. For example, I would expect a center of (0 32 0) but got (-10.383215, 32, 10.383215) instead. Any idea?