`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)))`

If 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))

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

Given that the area of a polygon of n sides circumscribed about a circle is to the area of the circumscribed polygon of 2n sides as 3:2 find 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 6 (b) 4 (c) 8 (d) 12

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

Let A_n be the area that is outside a n-sided regular polygon and inside its circumscribeing circle. Also B_n is the area inside the polygon and outside the circle inscribed in the polygon. Let R be the radius of the circle circumscribing n-sided polygon. On the basis of above information, answer the equation If n=6\ then A_n is equal to R^2((pi-sqrt(3))/2) (b) R^2((2pi-6sqrt(3))/2) R^2(pi-sqrt(3)) (d) R^2((2pi-3sqrt(3))/2)

The difference between an exterior angle of (n-1) sided regular polygon and an exterior angle of (n+2) sided regular polygon is 6^(@) . Find the value of n

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)))