A circle is an assortment of focuses which are all on the periphery of the circle. Assuming that you use polynomial math and (x-h)^2 + (y-k)^2 = r^2 and the data contained in the directions (x,y) of every city, you can track down h, k and r. Then, at that point, r is the (equivalent) distance between every city and the focal point of the circle, where the new pinnacle will be assembled.
How would you make this construction to ensure that the location of the cities lie exactly on the circle?