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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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Q: What is the maximum number of distinct intersections of 30 different coplanar circles?
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