Question

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

(a) a cot (π/n)

(b) a/2 cot(π/2n)

(c) a cot (π/2n)

(d) a/4 cot(π/2n)

Answer 1

Answer:

a/4 cot(π/2n)

Step-by-step explanation:

Hope it helps you

Answer 2

Answer:

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

(a) a.cot(πn)

(b) a2cot(π2n)

(c) a.cot(π2n)

(d) a4cot(π2n)

I have partially solved this problem. I found the radii of the two circle individually but could not find the sum in terms of cot.

enter image description here

θ=180n

cotθ=ra2

r=cotθ.a2

sinθ=a2R

R=cosecθ.a2

r+R=a2.(cosec(180n)+cot(180n))

But the final answer is not in terms of cot, does anyone know how to express the entire thing in terms of cot. Thanks in advance.