Question

The ratio of the area of the inscribed circle to the area of circumscribed circle of an equilateral triangle is _____.

• A.
  $\frac{1}{4}$
• B.
  $\frac{1}{2}$
• C.
  $\frac{1}{6}$
• D.
  $\frac{1}{8}$

Answer 1

The correct option is A

$\frac{1}{4}$

$sin{30}^{\circ }=\frac{r}{R}$

$Arearatio$

$=\frac{\pi r^2}{\pi R^2}={\sin }^2{30}^{\circ }=\frac{1}{4}$