No two circles can intersect more than twice.
Each circle can intersect with each other circle.
Thus there ought to be 2 × 30 × (30 - 1) intersections.
However, this counts each intersection twice: once for each circle.
Thus the answer is half this, giving:
maximum_number_of_intersections = ½ × 2 × 30 × (30 - 1) = 30 × 29 = 870.
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They're concentric circles. But I don't think they even need to be coplanar in order to be concentric.
Tangent circles.
If they have a common centre, they are concentriccircles.
No, the sets and subsets can be any shape, but circles and rectangles are neater. Also, circles or rectangles will usually intersect in only one part whereas very wriggly shapes can have multiple intersections.
The intersections of two circles produces a lens shaped area with two edges. It looks like the shape of the shadow of an American football