If `I_n` is the area of `n-s i d e d` regular polygon inscribed in a circle of unit radius and `O_n` be the area of the polygon circumscribing the given circle, prove that `I_n=(O_n)/2(sqrt(1+((2I_n)/n)^2))`

Prove that: adj.I_n=I_n

Prove that: adj.I_n^-1=I_n

The ratio of the area of a regular polygon of n sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same is 3 : 4 . Then the value of n is

The ratio of the area of a regular polygon of n sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same is 3 : 4 . Then the value of n is

The number of diagonals of a regular polygon of n sides are:

Prove that n! (n+2)=n!+(n+1)! .

Find the radius of the circumscribing circle of a regular polygon of n sides each of length is a.

Find the sum of the radii of the circles, which are respectively inscribed and circumscribed about the a regular polygon of n sides.

A circle is inscribed in an n-sided regular polygon A_1, A_2, …. A_n having each side a unit for any arbitrary point P on the circle, pove that sum_(i=1)^(n)(PA_i)^2=n(a^2)/(4)(1+cos^2((pi)/(n)))/(sin^2((pi)/(n)))

Statement I perimeter of a regular pentagon inscribed in a circle with centre O and radius a cm equals 10a sin 36^(@) cm. Statement II Perimeter of a regular polygon inscribed in a circle with centre O and radius a cm equals (3n-5)sin ((360^(@))/(2n))cm, then it is n sided, where n ge3.