On the picture the middle of the small circles don't touch the big circle because of the interpolation.
If I get what you're asking, you are wanting to find the circle that would have the centers of each circle on it's circumference...?
What I did, is copy your image to my Autocad and drew the random circles over the top of yours as close as I could (since I didn't have your exact drawing).
Then I started by setting my osnap to center only. Then I started the pl (polyline command). I selected my start point as the center of the first circle, then I typed S (for second point) and then selected the center of the nearest circle, then I selected the center of the third circle, then I typed in S again and picked the fourrth circle then selected the fifth circle, then S again and selected center of 6th circle and then I selected the first circle as my end point and it created this circle.
Now, this won't always make a true circle if you have extreme random points, but at those times it will be more of a cam like appearance.
Is this what you were wanting? Or am I way off base here?