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Three circles of radius 5 are drawn so that each touches the other two. Find the radius R of the outer circle that touches all of the three circles, as shown in the figure below.

 

 Jan 4, 2021
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If we join the  ceters of these  circles, we have an equilateral tirangle with  sides of 10

 

We can compite  the  distance, D, from the  center of the large circle to the center of any of the small circle as

 

10^2  =  2D^2   - 2D^2 cos (120°)

 

100  =  2D^2  - 2D^2 (-1/2)

 

100  =  3D^2

 

100/3  = D^2  

 

D = 10/sqrt (3) 

 

So....the radius of the larger circle is   10/sqrt (3)  +  5   ≈  10.774    

 

 

cool cool cool

 Jan 4, 2021

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