2002 AMC 12B Problem 14

Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?

\mathrm{(A)}\ 8 \qquad\mathrm{(B)}\ 9 \qquad\mathrm{(C)}\ 10 \qquad\mathrm{(D)}\ 12 \qquad\mathrm{(E)}\ 16

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.