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Three circles have the same centre. The radius of the smaller circle is sqrt(3). The area of the region between the larger circle and the one in the middle is equal to the area of the smaller circle, and the area between the one in the middle and the smaller is equal to the area of the smaller circle. What is the radius of the larger circle?

 

 Jan 28, 2021
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Area of  smaller  circle   =  pi (sqrt (3))^2  = 3pi

 

Area  of middle  circle  - area of  smaller  circle =   area of  smaller  circle

Area of middle circle   -   3pi   =   3pi

Area of  middle   circle  =  6pi

 

So   

The  radius  of the  second  circle  must  be    sqrt (6)

 

And  the   area of the  outer  circle  -area of  middle  circle =  area of  smaller  circle

Area of  outer  circle  - 6pi  =   3pi

Area of  outer  circle =  9pi

 

So....the radius of the  outer  circle  must   =  sqrt (9)  =  3

 

cool cool cool

 Jan 28, 2021

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