Problem:
Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Each pair of circles has at most two intersection points. There are pairs of circles, so there are at most points of intersection. The following configuration shows that 12 points of intersection are indeed possible:
The problems on this page are the property of the MAA's American Mathematics Competitions