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I'm trying to generate a script/file in MS Excel where I can calculate the perimeter variation of growing intersecting circles. In my example there is three circles placed in a random pattern. They start at 1 mm radius and is then growing. I have managed to calculate the perimeter at initial conditions and when only "one-to-one" interaction occurs, see fig 1 and fig 2.

But my problem is when the circles are overlapping, and "taking away" the same perimeter, as my calculations are now, this is not accounted for and the perimeter is underestimated.

In short: I'm looking for a way to calculate the perimeter at any given time for these growing circles: (perimeter represented by solid line)

a Start conditions a After 1mm increase a After 2mm increase

Is there a way to mathematically determine the perimeter of three "merged" circles? Or is there any other nice software that would do such a thing?

Hope I have managed to describe my problem.

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