Question

Maximum number of points of intersection of 3 circles and 3 lines is:

• A. 21
• B. 9
• C. 27
• D. 3!

Answer 1

The correct option is C 27

3 lines intersect each other in ${}^3{C}_2=3$ points.
3 circles intersect each other in ${}^3{P}_2=6$ points.
Every line cuts 3 circles into 6 points. Therefore 3 lines cut 3 circles into 18 points.
Therefore, the maximum number of points=3 +6+18 =27