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What is the maximum number of distinct intersections of 30 different coplanar circles?
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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What are coplanar circles with the same center?
They're concentric circles. But I don't think they even need to be coplanar in order to be concentric.
What are two coplanar circles that intersect at exactly one point?
Tangent circles.
What are coplanar circles that have a common center?
If they have a common centre, they are concentriccircles.
Do we need to use circles and rectangles in venn diagram?
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.
What shape has two edges?
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
