Prove that the sum of the radii of the circles, which are, respectively, inscribed and circumscribed about a polygon of `n` sides, whose side length is `a ,` is `a/2 `cot`pi/(2n)`

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.

The ionic radii of N^(3-) , O^(2-) and F^- are respectively given by

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

A quadrilateral ABCD is such that one circle can be inscribed in it and another circle circumscribed about it, then tan^2(A/2) is equal to

Let T_n denote of the number of triangles which can be formed using the vertices of a regular polygon of n sides If T_(n+1)-T_n=21 then n is

Find the sum to n terms of the series in whose n^(th) terms is given by n^2+2^n

If alpha_1 and alpha_2 be the circular measure of the angles subtended by the arcs of lengths s_1,s_2 at the centres of the circles whose radii are a_1,a_2 respectively , then show that the angle subtended at the centre by the arc of length (s_1+s_2) of a circle whose radius is 1/n(a_1alpha_1+a_2alpha_2) will be n radians.

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

Find the sum to n terms of the series in whose n^(th) terms is given by (2n-1)^2

Let T_(n) denote the number of triangles which can be formed using the vertices of a regular polygon of n sides . If T_(n+1)-T_(n)=21 then find the values of n .