gretest number of point of intersection of 8 lines and4 circles
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gretest number of point of intersection of 8 lines and4 circles
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Each pair of line can at the max intersect at one point. Therefore if you have n lines there can be nC2 pairs each with 1 intersection. So nC2 intersections.
Similarly for each pair of circle can at the max intersect at 2 points. Therefore if you have m circles there can be mC2 pairs of circles each with 2 intersections. So the total number of intersections will be 2*mC2.
Also, a line and a circle can intersect at 2 points (at the max). Therefore if there are n lines and m circles there can be n*m combinations of lines and circles each with 2 intersections. Hence the total number of intersections will be 2*m*n.
Therefore the general formula for maximum number of intersections of n lines and m circles is
nC2 + 2*(mC2) + 2*m*n
So the total number of intersections in this case will be 8C2 + 2*(4C2) + 2*4*8 = 104
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