There are n points on a circle that are pairwise connected by a chord in the circle. What is the maximum and the minimum number of points within the circle that are intersections of the chords?
Finding the number of intersections of chords within a circle
3
$\begingroup$
combinatorics
geometry
-
0@HerngYi For the regular $n$-gon the number of intersections is given by sequence [A006561](http://oeis.org/A006561) but I don't believe that is the minimum e.g. for $n=7.$ – 2016-08-04
1 Answers
-1
To form a pair of chords that intersect, you need 4 points. Hence, that can be done in nC4 ways. There is only way to join the 4 points with two chords and form an intersection. Hence, the final answer is nC4.
-
0This doesn't answer the question because in some configurations the chords do not intersect inside the circle. – 2016-12-08