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Oct 2, 2013 at 11:44 comment added Vince Less difficult, but the shape of the original polygon would not be retained (and therefore not sure to be "within the originals", though scaling holes would produce similar issues).
Oct 2, 2013 at 11:38 comment added Martin From the centerpoints one could also buffer (the points) the relevant distance (trigonometry to calculate) to create a polygon with desired area, which then will be circular. However, it will require some hands-on work for each polygon.
Oct 2, 2013 at 11:34 history answered Vince CC BY-SA 3.0