A circle is circumscribed about an equilateral triangle, and that equilateral triangle is circumscribed about another circle. Then the ratio of perimeter of circumcircle to that of an in circle is

Question

A circle is circumscribed about an equilateral triangle, and that equilateral triangle is circumscribed about another circle. Then the ratio of perimeter of circumcircle to that of an in circle is

A. 4:3

B. 2:1

C. 3:4

D. 1:2

Answer: B

Solution:

Let the side of an equilateral triangle is ‘a’.

Then radius of a circumcircle is a/√3 and radius of an incircle is a/2√3.

The ratio of perimeter is a/√3 : a/2√3 = 2 : 1