`I_(n)` is the area of n sided refular polygon inscribed in a circle unit radius and `O_(n)` be the area of the polygon circumscribing the given circle, prove that `I_(n)=O_(n)/2(1+sqrt(1-((2I_(n))/n)^(2)))`

I_(n) is the area of n sided 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(1+sqrt(1-((2I_(n))/n)^(2)))

Prove that : 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

Prove that the area of a regular polygon hawing 2n sides,inscribed in a circle,is the geometric mean of the areas of the inscribed and circumscribed polygons of n sides.

If r is the radius of inscribed circle of a regular polygon of n-sides ,then r is equal to

The area of the circle and the area of a regular polygon of n sides and the perimeter equal to the circle are in the ratio of

In the following figure a wire bent in the form of a regular polygon of n sides is inscribed in a circle of radius a . Net magnetic field at centre will be

A circle of radius r is inscribed in a regular polygon with n sides (the circle touches all sides of the polygon). If the perimeter of the polygon is p, then the area of the polygon is

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)))