hard geometry question

Question

Four distinct points are chosen at random on a circle. LIne segments are then drawn connecting every possible pair of these points. Theses line segments divide the interior of the circle into how many  individual nonoverlapping regions of nonzero area?

 

 

 

A) 2

B)4

C)6

D)8

E)24

 

I keep on getting the answer c because I made a square connecting the points. However that answer is obiously wrong and I don't know how. I am seriously stuck and I need some major help on this. THANK YOU!!!!!!

Answer 1

Since the points are assigned randomly and you are asked for the number of non-overlapping regions, the answer must hold for equally spaced points.  Thus, you only need to deal with a square.

 

The lines are the sides of the square and its two diagonals.  There are four regions interior to the square and four regions outside of the square (one for each side of the square).

 

There is a total of eight regions.  Answer D is correct.