Question

gretest number of point of intersection of 8 lines and4 circles​

Answer 1

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

^_^

Answer 2

Step-by-step explanation:

The greatest possible number of points of intersection of 8 straight lines and 4 circles is 104.

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