Question

The greatest number of points of intersection of $8$ lines and $4$ circles is:

• A. $104$
• B. $64$
• C. $92$
• D. $96$

Answer 1

Answer: (A)

Two lines will intersect at one point. So max numbers of point of intersection are given by $8C_2$

Two circles will intersect on two points at max, so total number of point of intersections of circles can be $4C_2\times 2$.

Now we can take a circle, a line and they will also intersect on 2 points

so total we have

${}^8{C}_2$ + ${}^4{C}_2\times 2$ + $2\times 4\times 8=104$