Question

In a $△ABC$, if $b=2,\angle B={30}^o$, then the area of the circumcircle of $△ABC$ (in sq. units) is

• A. $\pi$
• B. $2\pi$
• C. $4\pi$
• D. $6\pi$

Answer 1

The correct option is C $4\pi$

Using sine rule

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R\Rightarrow \frac{b}{\sin B}=2R\Rightarrow \frac{2}{\sin {30}^{\circ }}=2R\Rightarrow 4=2R\Rightarrow R=2$

Area of circle $=\pi R^2$

$\Rightarrow A=4\pi$

So option $C$ is correct.