Suppose we have two circles of radius 2 each in the plane such that the distance between their centres is 2\sqrt 3 . The area of the region common to both circles lies between

Correct Answer is : 0.7 and 0.75

KVPY SA Exam 19-Nov-2017 Question Paper

Question : 63 of 80

Marks: +1, -0

Suppose we have two circles of radius 2 each in the plane such that the distance between their centres is

2√ 3

. The area of the region common to both circles lies between

Solution:

Let two circles are

x^2 + y^2 = 4\ &\ (x-2√ 3 )^2 + y^2 = 4

∴ equation of common chord is

x = √3

∴

A ( √3 , 1) , B( √3 , -1)

∠AC_1B = 60°

AB = 2 &

MC_1=√ 3

Required area = 2 [area of sector C

_1

AB – ar

∆C_1

AB]

=2[1/2×2^2×π/3-1/2×2×√3]

= .723

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