Question

I_n is the area of n sided regular polygon inscribed in a circle of unit radius and On be the area of the polygon circumscribing the given circle, prove that I_n = On/2(1 + √(1 - (21_n/n)²))

Answer 1

We know I_n = n/2r²sin(2π/n)(I_n is area of regular polygon)

⇒ 2I_n/n = sin(2π/n) (r = 1)

and O_n = nr²tan(π/2) {O_n is area of circumscribing polygon}