I'm finding it hard to find the answer to this problem, I suspect it is simple and I'm missing something.
Assume there are three circles with equal radius. The circumference of the circles intersect at one common point - that is, they are Johnson Circles. Their centers are also equidistant from each other; a triangle made from their centers would be equilateral.
In terms of the radius of the circles, what is the distance between any two circle's centers?
And before you get any ideas - none of the circles share a center.
For anyone coming across who says Maths like this has no practical application, this is for a Venn Diagram I'm coding where the circles can change their radius and it's important to enforce a middle segment or lack thereof in different situations, depending on data.