X1, X2,...,X9 are nine points on the circumference of circle O. Line segments are drawn connecting each pair of points.

Question

What is the largest number of different points inside the circle at which at least two of these line segments intersect? (Remember that the points are not necessarily evenly spaced around the circle.)

Answer 1

google is your friend. You can start here:

http://mathforum.org/library/drmath/view/51708.html