The problem of determining the circle of best fit to a set of points in the plane (or the obvious generalisation ton-dimensions) is easily formulated as a nonlinear total least squares problem which may be solved using a Gauss-Newton minimisation algorithm. This straightforward approach is shown to be inefficient and extremely sensitive to the presence of outliers. An alternative formulation allows the problem to be reduced to a linear test squares problem which is trivially solved. The recommended approach is shown to have .the added advantage of being much less sensitive to outliers than the nonlinear least squares approach.