The sum of the radii of inscribed and circumscribed circles

• Trigonometry

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is

1. a/2 cot(π/2n)
2. a/4 cot(π/2n)
3. a cot(π/n)
4. a cot(π/2n)

Answer

tan (π/n) = a/2r

sin (π/n) = a/2R

r + R = a/2[cot π/n + cosec π/n]

The correct option is A.