The Maximum number of points of intersection of 4 distinct circles and 8 distinct straight lines is
1)66
2)64
3)104
4)40
Can anyone please help me to solve this problem?
My attempt : I have seen this link–Maximum number of points of intersection. But I can not understand how they are so sure that all intersection points are distinct.
Best Answer
I will construct an explicit example. Take the following two configurations:
The second configuration is the eight-line solution to my generous lazy caterer problem. Now scale down the eight-line configuration so that all its intersections are inside the intersection of all the four circles (the small squarish region). If it happens that there is a multiple intersection, we can just tweak to remove it. Then we are guaranteed that every line intersects every circle twice, obtaining the maximum of $104$ intersections.
This is the result:
To generalise to any number of circles and lines: