+0  
 
0
53
2
avatar

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 25, 2021
 #1
avatar+116126 
+1

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

 

 

cool cool cool

 Jan 25, 2021
 #2
avatar+1035 
+3

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 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Square side = 14             small radius r = 3             big radius R = ?

 

The distance between the centers of the small circles is 8 units.

 

So, we have       42 + (11 - R)2 = (3 + R)2          R = 32 / 7    or   R ≈ 4.57 

 

 Jan 25, 2021

52 Online Users

avatar
avatar