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Find a circle when given three or more points

given: $(x_1, y_1), (x_2, y_2), (x_3, y_3), \ldots ,(x_n, y_n)$

Find center of circle coordinate $(x_0, y_0)$

I can find circle using three points.

But given more points, I can't find circle method.

Can it be explained with specific methods and equations?

And is it correct to find the radius and minimize the error of each radius using least square?

Samuel Adrian Antz
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곧미남
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    The center of the circle must be on the perpendicular bisector of any two points on the boundary of the circle. This is why only $(3)$ points are needed. You take the intersection of two lines. If you are given more than $(3)$ points, just pick any three of the points, at random, ignore all of the rest of the points, and apply the method that pertains to knowing only $(3)$ points. – user2661923 Jul 01 '22 at 03:16
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    Given more than three points, there is no reason for them to lie in the same circle. If they do, then use any three distinct points. – pancini Jul 01 '22 at 03:28
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    Have a look at https://math.stackexchange.com/questions/4246653/get-the-best-fit-circle-if-radius-is-specified-constrained/4250768#4250768 – Claude Leibovici Jul 01 '22 at 03:56

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