CirclePoints and CircleThrough

Question

$Version 

12.2.0 for Microsoft Windows (64-bit) (December 12, 2020)

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For points (located on a unit circle),

pts = CirclePoints[11]

$$\left\{\left\{\sin \left(\frac{\pi }{11}\right),-\cos \left(\frac{\pi }{11}\right)\right\}, ...\right.$$

Graphics[{
  Blue, Circle[],
  Red, PointSize[0.02], Point@pts
  }]

Question(s)

• Is this version related or is there a limit on how many points the CircleThrough algorithm can fit?

• For fitting random points to the best-fit circle, I have already looked at this post. I wonder if any built-in function has been provided since?

Note(1) For 10 points it works with pts//N. For 11 pts, it doesn't work with either variation.

Any help will be greatly appreciated.