Given a number n, we need to find the maximum number of times n circles intersect.
Input : n = 2 Output : 2 Input : n = 3 Output : 6
Description and Derivation
As we can see in above diagram, for each pair of circles, there can be maximum two intersectuib points. Therefore if we have n circles then there can be nC2 pairs of circles in which each pair will have two intersections. So by this we can conclude that by looking at all possible pairs of circles the mathematical formula can be made for the maximum number of intersection by n circles is given by 2 * nC2.
2 * nC2 = 2 * n * (n – 1)/2 = n * (n-1)
- Ratio of the distance between the centers of the circles and the point of intersection of two direct common tangents to the circles
- Ratio of the distance between the centers of the circles and the point of intersection of two transverse common tangents to the circles
- Maximum points of intersection n lines
- Maximum possible intersection by moving centers of line segments
- Maximum number of segments that can contain the given points
- Count maximum points on same line
- Find the maximum possible distance from origin using given points
- Angular Sweep (Maximum points that can be enclosed in a circle of given radius)
- Minimum number of points to be removed to get remaining points on one side of axis
- Steps required to visit M points in order on a circular ring of N points
- Count of obtuse angles in a circle with 'k' equidistant points between 2 given points
- Ways to choose three points with distance between the most distant points <= L
- Prime points (Points that split a number into two primes)
- Number of Integral Points between Two Points
- Path in a Rectangle with Circles
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
Improved By : Sam007