+1452 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!
+129933
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
