Question

The area of triangle formed by joining the centres of three congruent externally touching circles, is $49\sqrt{3}sq-cm$ , then find the radius of circle.

• A. $\sqrt{7}cm$
• B. $7cm$
• C. $7\sqrt{3}cm$
• D. $4\sqrt{3}cm$

Answer 1

Answer: (B)

$7cm$

Let the radius of each circle be $r$

The length of side of an equilateral triangle formed by the centers of three congruent externally touching circles is $2r$

The area of triangle is $\frac{1}{2}\times 2r\times 2r\times sin\left({60}^0\right)=\sqrt{3}{r}^2=49\sqrt{3}$

$\Rightarrow r^2=49$

$\Rightarrow r=7$

Therefore the radius of circle is $7$cm

So the correct option is $B$