Question

The ratio of area of the circumcircle to that of the incircle in equilateral triangle is

• A. $2:1$
• B. $3:2$
• C. $4:1$
• D. $9:1$

Answer 1

Answer: (C)

$4:1$

Let the side length of the equilateral triangle $=x$

Area of the in-circle$=\frac{1}{12}\pi x^2$

Area of circumcircle $=\frac{1}{3}\pi x^2$

so ratio circumcircle area / incircle area $=\frac{\frac{1}{12}\pi x^2}{\frac{1}{3}\pi x^2}=\frac{4}{1}=4:1$