Let m be the number of the overall points of n circles

[MM]

Let m be the number of the overall points of n circles. Let all their overall points are finite number. Find the maximal value of m.

[shyamjayakannan]

To find the maximum number of intersection points of n circles, we need to count all the distinct pairs of circles and multiply that by 2 because each pair gives 2 intersection points.

So, [tex]m=2{}^nC_2=2\times\frac{n!}{2!(n-2)!}=\boxed{n(n-1)}[/tex]