Question

The greatest possible number of points of intersection of 8 straight lines and 4 circles in a plane is

• A. 32
• B. 104
• C. 76
• D. 100

Answer 1

Answer: (B)

104

The number of points of intersection when circles intersect $=2\times \left(\begin{array}{c}4\\ 2\end{array}\right)=12$
multiplied by 4 because we have to calculate greatest possible no. of intersection and in that case circles can intersect at 2 points.
The number of points of intersection of circle and straight line $=2\times \left(\begin{array}{c}8\\ 1\end{array}\right)\times \left(\begin{array}{c}4\\ 1\end{array}\right)=64$
circle and straight line intersect at 2 points at most.
The number of points of intersection straight lines$=1\times \left(\begin{array}{c}8\\ 2\end{array}\right)=28$
since two straight lines intersect at at most one point.
Hence greatest possible number of intersection$=(12+64+28)=104$