Coding Problem with growing circles

Hello,

I'm trying to code a scenario that goes something like this:

The centers of a bunch of circles is randomly initialized. The rate at which the radii of each circle is also randomly initialized. And then I wish to account for the following situations:

1) In one scenario, the circles are allowed to grow until they touch another circle.

2) In another scenario, the circles are allowed to grow until they reach a certain percent overlap with any other circle; or in other words they are allowed to share a common area with other circles up to a certain percentage of their own area, which is user-defined.

Initializing the positions and growing the circles is ok, but how to stop growing them is what I have issues with. Any help would be greatly appreciated.

Answer 1

[Walter Roberson]

https://mathworld.wolfram.com/Circle-CircleIntersection.html shows the calculation for overlap area step by step.