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Three circles fit inside a square as shown where two small circles touch a large circle. Given that the radius of the small circles is 3 and the side length of the square is 14, find the radius of the larger circle 

 

 Jan 28, 2022
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Let the center of the  large circle  be   =  (7,R)

 

Then the  center of   one of the  small circles   is  (11, 11)

 

So  the square of the distance   between  these two points  is   (R + 3)^2

 

So

 

(7-11)^2  + (11  - R)^2  =   (R + 3)^2

 

4^2  + R^2   -  22R + 121 =   R^2  + 6R  + 9     simplify

 

137 - 22R  =  6R + 9

 

137  - 9  =  28R

 

128  = 28R

 

128/28 =  R  =  32/7

 Jan 28, 2022

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