# CAT Practice : Mensuration

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Area of a circle.

## Three Circles

Q.15: Three circles with radius 2 cm touch each other as shown :-

Find the area of the circle, circumscribing the above figure.

1. 3${\pi}$(4+√3)2
2. ${\frac{\pi}{2}}$(4+2√3)2
3. ${\frac{\pi}{4}}$(4+2√3)2
4. ${12\pi - \frac{\pi}{2}}$(4+2√3)2

Choice B. ${\frac{\pi}{2}}$(4+2√3)2

## Detailed Solution

Diagram -

Let r’ be the circumradius of ∆ABC,

∴ R = 2 + r’

We know from the properties of equilateral triangle

r’ = ${\frac{Sides}{√3}}$ = ${\frac{4}{√3}}$

(This can easily be derived using trigonometry. However, please remember this formula. It is useful at places)

∴ R = 2 + ${\frac{4}{√3}}$

∴ Area = ${\pi*R^2 = \pi* \frac{(2√3+4)^2}{√3^2}}$

= ${\frac{\pi}{3}}$*(4+2√3)2

Choice (B) is therefore, the correct answer.

Correct Answer: ${\frac{\pi}{2}}$(4+2√3)2

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## More questions from Mensuration

Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.