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I've been trying like mad to make an arc from two concentric circles connected by lines, by first joining the lines and the circles and then deleting the circles' arcs between them, as in the image:
But I can't seem to get it for the life of me, no matter what I do. I try to add extra nodes in the circle and then join selected nodes between the circle and the line, but it never comes through! Am I missing something?
This is not an exact answer to your question, but a quicker way to create the shape you described.
Draw the circles (grey), and a block (red) and align them as you like.
Then follow these 2 Steps:
ctrl+-)What you want to do is cut the circles with a path (the lines). The lines are temporary and are just used to get the nodes onto the circles in the correct spot. Next you need to combine the two circles (which will become paths after being cut) so that you can manipulate their nodes together.
Step by step
Extend those two lines up and down to ensure that they fully intersect both circle paths (these are temporary lines, so they worry about it looking funny)
Duplicate each of those lines once with Ctrl+D. There are now 4 lines (two on each side)
Select one of the lines, then select a circle, then click Path > Cut Path.
Repeat the above step with the other 3 lines. You will now have nodes on your circle exactly where those lines were and the lines will be gone.
Select both circles, then click Path > Combine
Using the Node Tool F2, delete the select of the path between the two nodes. You've be left with something that looks like this:
