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# Geometry problem

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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?   Thanks!

Mar 29, 2018

### 1+0 Answers

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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   Mar 29, 2018