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?
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