# Two Wheel Belt

Two Wheel Belt

A classic trigonometry problem asks for the length of a belt wrapped around two wheels. The radii of the two wheels are and . The wheels are units apart.

x

x+y

z

Let A and C be the two arcs of the belt and let B be one of the two segments joining the ends of the arcs. B is an exterior tangent to both circles. Then the lengths of A, B, and C are and .

2θx,

2(2x+y+z)sin(θ),

2(π-θ)(x+y)