2009
Problem - 2650
Three circular cylinders are strapped together as shown. The cross-section of each cylinder is a circle of radius 1. Presuming that the strap used to bind the cylinders together has no thickness and no extra length, how long is the binding strap?
The answer is $\boxed{6+2\pi}$. Hint: the radius connecting the center and the tangent point must be perpendicular to the tangent line.