Hi,

I'd like to make a ring with the upper-right and left segments cut
out. How do I cut out a small segment of the ring?

Hi.

There is several ways to do this, dependent on how accurate you want it to be.

This is a simple solution:
* Draw the ring.
* Select the ring and click: Path -> Object to Path
* Select node tool. Make sure the ring is selected. You will see four nodes.
* Select the two nodes that have a the segment between (or you can just select the segment - between nodes)
* Click the button with help text "delete segment between two non-endpoint nodes". On my screen I find the button on upper left on the screen, the sixth button in that toolbar of blue node-buttons.
* Voila

Another way to do it:
After you draw the circle with the Ellipse tool, grab the tiny circle handle (right side of circle) and drag it around. If you keep the mouse/pointer to the inside of the circle, you'll be drawing an arc. If you move the pointer outside the circle as you drag, you'll get more of a wedge (called a "segment" on the tool control bar). Or the buttons on the control bar can switch from one to the other.

I actually prefer Grobe's method, but thought I'd mention this one too