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.