AMC 12 2002b 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?

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