Polygonal designs and intersections

[Blighty]

Create a circular path
There are various ways to this. There is the arakne path shape creator, but it does not work on my Gimp. So I use another one, shape-path.
It can also be done by creating a circular selection and then Select > To Path. Not as neat as using the path tools.

Create the second, smaller circle
Either work from scratch, or duplicate the first path and resize it with the Scale Tool set to path mode.

You now have something like this:
https://imgur.com/a/7wkuLIA

Move small circle into position
Use the Move Tool, set to path mode, to move the small circle so that the centre of the small circle is on the big circle.

Add additional nodes to the big circle.
In the Paths Dialogue, select the big circle. The path will change to red.
Ctrl-Click on the intersection an intersection of the big and small circle. This will add a new node.
Do the same for the other intersection.

You now have something like this:
https://imgur.com/a/KrWp4mZ

Delete portion of big circle
Using the Path Tool, click on the portion of the circle between the 2 new nodes to select it.
Shift-Ctrl-Click it to delete that portion.

You now have this:
https://imgur.com/a/jJxVv0o

If necessary, right click on a path in the Paths Dialogue and do Merge Visible Paths

Paths are now complete.
Use Edit > Stroke Path to stroke the path.

For more information on paths, see:
https://www.gimp-forum.net/Thread-Working-with-Paths