The greatest possible number of points of intersection of 8 distinct straight lines and 4 distinct circles is

Step-by-step solution

To determine the maximum number of intersection points among 8 distinct straight lines and 4 distinct circles, consider all possible pairwise intersections. Intersections between lines: Each pair of lines intersects at most once, yielding 8 2 = 28 points. Intersections between circles: Each pair of circles intersects at most twice, giving 2 4 2 = 12 points. Intersections between lines and circles: Each line and circle intersect at most twice, contributing 2 8 4 = 64 points. Summing these independent cases, the tota