Hello web2.0calc, I was doing AoPS Alcumus when I found this question

Ten circles are all the same size. Each pair of these circles overlap but no circle is exactly on top of another circle. What is the greatest possible total number of intersection points of these ten circles?

This was soo difficult. How would it work? But then I found out a critical point:

- Every unique pair of circles has 2 intersections.

WOW! This was life saving. There would be C(10, 2) pairs of interesctions, which is 45.

As each is a pair, we have to multiply by two to get the individual interestctions, whic is **90!**

Thank you for coming to my TED talk.

Guest Jun 18, 2020