Finding a circle that intersects 'n' other circles (at least once) whilst minimizing its radius

Dear MATLAB community,

I am trying to identify a method to find a circle, with initially unknown centre coordinates (x,y) and radius (r), that intersects (or is at least tangential to) 'n' other circles with known radii and centre coordinates. However, a further caveat to this problem is that the radius of the unknown circle should also be minimized.

To give a little more information, the unknown circle represents a trace of positions of an object as it is rotated about a point i.e. the center of the unknown circle. The 'n' known circles are formed based on measurements, where the center coordinates represent different locations to which a length measuring device is affixed, and the radii represent the distance between these points and circular motion path described by the unknown circle. In terms of general appearance, the known circles are distributed around the periphery of the unknown circle, although this may not always be the case.

Due to measurement noise and other uncertainties, it is unlikely that there is a direct solution; however, it may help to know that two dimensions is sufficient to characterize this problem due to the fact that all circle centers are approximately coplanar. For the time being, I think it should be essential that the fitted circle at least touch each of the 'n' surrounding circles.

I wonder if perhaps this might be reduced a least squares problem?

Any small hints or wise words from past experience would be greatly appreciated.

I look forward to further discussion!