Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?
I need to count how many pairs of circles can intersect, and then multiply that by the number of points where each pair can intersect. To find the number of pairs, I can use the combination formula: nCr = n! / (r! (n - r)!), where n is the number of circles and r is 2. So, the number of pairs is 4C2 = 4! / (2! 2!) = 6. For each pair of circles, they can intersect at most twice, unless they are coincident, which is ruled out by the problem. So, the maximum number of intersection points is 6 times 2, which is 12. 