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(4+√3)2
    2. (4+2√3)2
    3. (4+2√3)2
    4. (4+2√3)2

 

  • Correct Answer
    Choice B. (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’ = =

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

∴ R = 2 +

∴ Area =

= *(4+2√3)2

Choice (B) is therefore, the correct answer.

Correct Answer: (4+2√3)2



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More questions from Mensuration

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  2. Spheres
  3. Circles and Chords
Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.