Intersection Points in a Circle
A chord is drawn between every two point on the perimeter of a circle. There are n points on the perimeter. Every two chords intersect at a point either on the perimeter or inside the circle.
(a) Determine the number of chords drawn
-- (n choose 2)
(b) What is the maximum number of intersection points inside the circle?
-- For this one I keep ending up in an infinite loop and drawing increasingly harder circles. Can someone point me in the correct direction?
I have (n*(n-1)) + (n-3)n - n + (n-4)n - n....
I don't know how to show when to stop.
(c) What is the maximum number of chords which can go through any single intersection point inside the circle?
--I don't even know where to begin here.
Any help would be greatly appreciated!!!