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  4. In a triangle ABC, if b=2, angle B =30°, then the area of the circumcircle of triangle ABC (in sq units) is

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

ManipalManipal 2016

Solution:

since, $R=\frac{b}{2 \sin B}=\frac{2}{2 \sin 30^{\circ}}=\frac{2}{1}$
$\therefore $ Area of circumcircle $=\pi R^{2}=\pi(2)^{2}=4 \pi$ sq units