Hello, Kantonar!

As tkhunny said, it's an excellent diagram . . . Thank you!

Two pulleys are connected by a belt.

The radii of the pulleys are 3cm and 15cm.

The distance between the two centers is 24cm.

Find the total length of the belt.

Code:

```
* * *
* *
* *
* *
* * *
* A * * *
* * * 24
* : * * B *
C+ - - - - - - - * - - * *
* 15: * * : *
* : * :3
* : * * : *
* * * - - - - - - - - * * *
E D
```

Draw the line of centers \(\displaystyle AB\,=\,24\)

Draw a horizontal segment \(\displaystyle BC\).

In right triangle \(\displaystyle ABC:\,AB\,=24,\;AC\,=\,12\)

\(\displaystyle \;\;\)Hence: \(\displaystyle \,BC\,=\,12\sqrt{3}\,=\,DE\)

\(\displaystyle \;\;\) Moreover: \(\displaystyle \,\angle ABC\,=\,30^o\)

Extend \(\displaystyle AB\) to \(\displaystyle F\) on circle \(\displaystyle B\)

We find that: \(\displaystyle \angle FBD\,=\,60^o\)

Extend \(\displaystyle BA\) to \(\displaystyle G\) on circle \(\displaystyle A\).

We find that: \(\displaystyle \angle GAE\,=\,120^o\)

And that is enough to determine the curved portions of the belt.