Three wooden equilateral triangles of side length 18 inches

are placed on axles as shown in the diagram to the right. Each axle

is 30 inches from the other two axles. A 144-inch leather band is

wrapped around the wooden triangles, and a dot at the top corner is

painted as shown. The three triangles are then rotated at the same

speed and the band rotates without slipping or stretching. Compute

the length of the path that the dot travels before it returns to its

initial position at the top corner