The centers of three pulleys are located at the vertices of a right triangle whose sides are 5 inches, 12 inches, and 13 inches. The radii of the pulleys are 1 inch (located opposite of the 12inches side), 2 inches (located opposite to the 13inches side), and 3 inches. Find the length of the belt that wraps around all three pulleys.

Question

The centers of three pulleys are located at the vertices of a right triangle whose sides are 5 inches, 12 inches, and 13 inches. The radii of the pulleys are 1 inch (located opposite of the 12inches side), 2 inches (located opposite to the 13inches side), and 3 inches. Find the length of the belt that wraps around all three pulleys.

Answer 1

There is a handy video at

www.youtube.c om/watch?v=qfZAFQ4so9c

If the two pulleys have radii r and R, and their centers ar separated by a distance D, then the length of belt needed is
2√(L^2 - (R-r)^2) + 2(R+r)θ
where cosθ = (R-r)/L

Now, you have three pulleys, so you will have to adjust things a bit, but the video should make it clear how to do that. Post your work if you get stuck.