Npoints lie on a circle. you draw lines connecting all the points to each other. these lines divide up the circle into a number of regions. how many regions is this? assume that the points are scattered in such a way as to give the maximum number of regions for that n.

In the question,

There are 'n' points on the circle.

For making the maximum number of regions we can do that by selecting 2 points from the given number of points.

i.e.

And,

By selecting 4 points from the given number of points we get the extra regions formed on the intersection of the chords with each other.

i.e.

And, 1 more region.

So, we can write it as,

Therefore, the number of regions formed from the 'N' points are,