What's the length of the belt?

Using the above diagram $y = 12 \implies \tan(\theta) = \dfrac{12}{5} \implies \theta = \arctan(\dfrac{12}{5}) \implies$

$L_{1} = 6(2\pi - 2\theta) = 12(\pi - \theta)$ and $L_{2} = 2\pi - (\pi - 2\theta + \pi) = 2\theta$

$\implies L = 24 + 12\pi - 12\theta + 2\theta = 2(12 + 6\pi -5\theta) = 2(12 + 6\pi + 5\arctan(\dfrac{12}{5}))$ $\approx \boxed{49.9390597721275189}$