I am not sure were to start on this problem, please help. Place n points on a ci

Question

I am not sure were to start on this problem, please help.

Place n points on a circle in a plane and make all possible chords connecting the n points with the constraint that no three chords intersect at a point inside the circle. (If three chords happen to intersect, one of the six points determining the chords can be moved slightly.) The chords and the circle create regions whose boundaries are the chords and possible segments of the circle. Define R(n) to be the number of these regions created from n points on the circle. Determine with proof a closed formula for R(n).

Explanation / Answer

There is a fairly simple solution involving graph theory if that is okay with you. I can look for a more combinatorial solution if that is what you're after.

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