Define Polygon radius so they don't overlap on Surface

Hey guys,

I'm working on a function to map Polygons with different amount of segments onto a surface. My Problem is, I would like to define the radius of the polygons by the distance to the next one...

My idea:

I dont wan't them to overlap, but i want the polygons to be as big as possible without the radius being bigger than a third of the length of one center point of the polygon to the next...

Hope you can help me how to build it...

Greets Marcus