Suppose we have two circles of radius 2 each | vedclass

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Question

(c)

Given,

Two circle each of radius is $2$ and difference between their centre is $2 \sqrt{3}$

$A B=2 \sqrt{3} \Rightarrow A C=\frac{1}{2} A

Vedclass · Accepted Answer

$0.7$ and $0.75$

Vedclass · Answer

(c)

Given,

Two circle each of radius is $2$ and difference between their centre is $2 \sqrt{3}$

$A B=2 \sqrt{3} \Rightarrow A C=\frac{1}{2} A B$

$A C=\sqrt{3}$

$\operatorname{In} 	riangle A P C, \quad \cos 	heta=\frac{A C}{A P}=\frac{\sqrt{3}}{2}$

$	heta=30^{\circ}$

Area of common region

$=2($ Area of sector $-$ Area of $	riangle A P Q)$

$=2\left(\frac{60}{360} 	imes \pi(2)^2-\frac{1}{2} 	imes(2)^2 	imes \sin 60^{\circ}ight)$ $=2\left(\frac{4 \pi}{6}-\frac{4 \sqrt{3}}{4}ight)$

$=2\left(\frac{2}{3}(3.14)-(173)ight)$

$=2(209-173)=2(0.36)=0.72$

$	herefore$ Area of region lie between $0.7$ and $0.75$.

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

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