Ratio of the areas of the circumcircle and the incircle of an n-sided regular polygon

Question:

To find the ratio of the areas of the circumcircle and the incircle of an n-sided regular polygon.

Solution:

Result:

The ratio of the areas of the circumcircle and the incircle of an n sided regular polygon is square of the secant ratio of (pi divided by the number of sides of the regular ploygon).

Note:

The ratio of the areas of the circumcircle and the incircle of an n-sided regular polygon is independent of size of the side. It depends only on the number of sides.

© Rishabh Bidya