Find the approximate center of a circle passing through more than three points

Consider n point $(x_1,y_1), (x_2,y_2),\ldots, (x_n,y_n)$. For $n = 3$ it is easy to find the center of the circle passing through the three points. I wanted find the approximate center of the circle passing through more than three points.

The application is as follows. I have circles on a sheet of metal. I can poll different points on the circle to get the their co-ordinates. By polling three points on every circle I can predict the co-ordinates of the center. But I wanted to improve the accuracy of the prediction. A Google search reveals only the center of the passing through three points.

Edit 1: In response to Hoda's comment, I am adding that the measurements related to the points on the circle have errors. The objective is to minimize the error in the position of the center by polling more points on the circle.

One can find on the web several methods of cercle fitting. Most of them are itterative. A straightforward method, without trial and error process, is described pp.12-13 in the paper "Régressions coniques, quadriques, circulaire, ..." : http://www.scribd.com/JJacquelin/documents No need to read the theoretical part written in French. Just apply the formulas (1), (2) and (3) which allows to very easily compute the coordinates of the center and the radius of the fitted circle. A numerical example is provided page 15.

Recalling the circle equation with center $(h,k)$ and radius $r$

$$ (x-h)^2+(y-k)^2 = r^2 .$$

The above equation has three unknowns which can be determined uniquely by knowing three points lie on the circle. However, if you have more than three points, then you may need to appeal to least squares method. See related technique.