Question

$ABC$ is a triangle with $\angle A=30°$, $BC=10$cm. The area of the circumcircle of the triangle is

• A. $100\pi$ sq cm
• B. $5$ sq cm
• C. $25$ sq cm
• D. $100\frac{\pi }{3}$ sq cm

Answer 1

The correct option is A

$100\pi$ sq cm

Explanation for the correct option:

Step 1. Find the area of circumcircle of the triangle:

Given, $ABC$ is a triangle with $\angle A=30°$, $BC=10$cm.

Let $O$ be the center of the circle

$\therefore \angle BOC=60°$

Also, $OB$ and $OC$ are the radius

$\therefore \angle OBC=\angle OCB=60°$

$\Rightarrow$$△OBC$ is an equilateral triangle

The radius of circle $=OB=OC=BC=10cm$

Step 2. Area of the circumcircle $={\mathrm{\pi r}}^2$

$$\begin{gathered} =\pi {\left(10\right)}^2 \\ =100\pi \end{gathered}$$

$\therefore$Area of circumcircle $\mathbf{=}\mathbf{}\mathbf{100}\mathbf{}\mathit{\pi }$ square cm

Hence, Option ‘A’ is Correct.