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Six small circles, each of radius 3 units, are tangent to a large circle as shown. Each small circle also is tangent to its two neighboring small circles. What is the diameter of the large circle in units?




 Mar 29, 2018


Connecting the centers  of the smaller circles  forms a hexagon  with  sides  of  6  units


But segments drawn from the center of the larger circle to each of these  6 centers  will form 6 equilateral triangles......so....a side of one of these triangles =  the side of the hexagon  =  6 units  (1)


And the distance from  a smaller circle center to the edge of the larger circle  = the radius of a smaller circle   = 3 units   (2)


So....the radius of the larger circle  =  (1)  + (2)  =    6 + 3  =   9 units


So...its diameter  =  2 * 9    =    18 units



cool cool cool

 Mar 29, 2018

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