Maximum Number of Points of Intersection of 10 Circles

The question asks about the maximum number of points of intersection of 10 circles. To answer this question, we need to consider the possible combinations of circles that can intersect with each other.

Formula for Maximum Number of Points of Intersection

The formula for the maximum number of points of intersection of n circles is:

N = n(n-1)/2

where N is the maximum number of points of intersection and n is the number of circles.

Applying this formula to the given problem, we get:

N = 10(10-1)/2
N = 45

This means that the maximum number of points of intersection of 10 circles is 45.

Explaining the Formula

The formula for the maximum number of points of intersection of n circles can be derived as follows:

- Each pair of circles can intersect at most two points.
- There are n(n-1)/2 pairs of circles.
- Therefore, the maximum number of points of intersection is N = 2n(n-1)/2 = n(n-1).

This formula is useful in solving problems that involve finding the maximum number of points of intersection of circles or other geometric shapes.

Conclusion

In this problem, we used the formula for the maximum number of points of intersection of circles to determine that the maximum number of points of intersection of 10 circles is 45. This formula can be applied to other similar problems to find the maximum number of points of intersection of geometric shapes.

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