# Regular Polygon

A regular polygon is a polygon which has all its sides equal and all its angles equal.

- Each interior angle of a regular polygon of
*n*sides is right angles = radians. - The circle passing through all the vertices of a regular polygon is called its
*circumscribed*circle. If*a*is the length of each side of a regular polygon of*n*sides, then the radius*R*of the circumscribed circle is given by . - The circle which can be inscribed within the regular polygon so as to touch all its sides is called its inscribed circle.
*a*is the length of each side of a regular polygon of*n*sides, then the radius*r*of the inscribed circle is given by - The area of a regular polygon is given by Î” =
*n*Ã— area of triangle*OAB*

# Inequality

In Î”

*ABC*, cos*A*+ cos*B*+ cos*C*â‰¤Also cos

*A*+ cos*B*+ cos*C*= 1 + 4â‡’

In Î”

*ABC*,*r*= 4*R*â‡’*R*â‰¤ 2*r*