How to find center of the circle/ellipse if the data points are in curved coordinates system(Horizontal - AltAz)

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I have 6 points with their coordinates in the Cartesian plane, XY, located on one side of a circle. Using the least square method it is relatively easy to fit a circle to those 6 points and to find the radius and the center of the fitted circle again in XY coordinates.. However, I also have Altitude Azimuth coordinates for those 6 points, because those points are on the sky, so I was wondering is it possible to fit a curve to those curved coordinates and then find the center of that circle?