What is the maximum number of regions can be there by connecting six points on a circle?

Example

6 points, 31 regions, see picture below:

There are n lines in a plane ( may or may not be concurrent ) . Find out the maximum and the least number of regions that can be formed ?

Triangle ABC is stuck in a circle. Its points are on random areas on the circumference of the circle. What is the probability of the triangle covering the centre of the circle?

A unit circle is divided into 12 congruent regions, as shown. What is the perimeter of one of these regions?

In the figure square ABCD is inscribed in a circle. EFGH is also a square with points E, F on circle and G, H on side of bigger square. Find the ratio of the areas of the bigger square to the smaller square?

How many squares can be formed in the following image by connecting four points of 8x8 grid?