The greatest number of points of intersection of 8 straight lines and 4 circles are?
My attempt:Assuming every line cuts all the four circles at two points each, the points of intersection of lines with circles=64.
Now, each circle cuts the other 3 circles at 6 points.Then points of intersection of circles is 6*4=24 making total number of points of intersection 88. The text book answer is 104. How is that?
[Math] Maximum number of points of intersection
permutations
Best Answer
The number of intersections of lines with lines is $7+6+5+4+3+2+1={8 \choose 2}$ and the number of intersection of the circles with circles is $6+4+2=2 {4\choose 2}$. This is because every line intersects with every other line and every circle intersects with every other circle. Your calculations on the number of intersections of lines with circles is correct at 64.