I am trying to create the largest possible circle inside a polygon including its perimeter and area size. I created via minimum boundary geometry the smallest possible circle outside a polygon (see image) and want to do some calculation with its largest circle inside the polygon. I have a shapefile of 25 polygons. Each has to have its own largest circle. This circle can be anywhere in the polygon, not necesserily at the centre since my polygons are uneven.
I tried looking at Find maximum radius of circle that will fit within an irregular polygon? but it was no success. I have the same problem as the OP.
I have worked up an answer in ArcMap and using ET Geowizards (as it is what I have access to but I think the same tools exist in ArcMap but require more than a basic license):
I haven't fully tested this so, maybe I missed a polygon shape that wouldn't work (conceptually I can't think of one). The bottom left one in the rectangle is interesting because the circle could be anywhere down the polygon and be just as valid. I guess it is at the top because the tool start works systematically top left to bottom right.
Some term this is as girth and University of Connecticut has developed a free geoprocessing tool (Shape Metrics) to calculate this among many other shape metrics. This is mentioned in the link as an index but it is quite easy to find the radius from the formulae given. You can download it from the link, https://clear.uconn.edu/tools/Shape_Metrics/Shape%20Metrics.zip