First, you need to decide for yourself what “exact” means. +/- 0.000? +/- 0.003? +/- 0.005"? I predict that your ring isn’t perfect so you might want to give yourself a little leeway. Also, the laser beam is conical so your slot isn’t going to be exactly the same size at the top and the bottom.
Echoing what @esmith says … you need to estimate your kerf (i.e., the material loss along the cut line due to the burning of the laser). I run things where precision matters and unfortunately, testing it is the only way to be sure. The kerf depends on the material, the laser and your cut settings. If you just blast the living daylights out of your piece you will get a lot more kerf. And the kerf can vary from day to day as the laser head gets dirty and/or out of alignment. You need to run your tests on the same day that you plan to cut your final object.
IIWM, I’d make some test cuts with a 1 inch square. Vary the settings until you get an edge finish you like. Measure the 1" square and its matching 1" hole after cutting and that will tell you how much kerf you’re getting. For the outside of the circle, you’ll need to add that much kerf to your dimension.
I’d also run a test of the ring slots. Your kerf is likely to be somewhere between 0.008" inches and 0.014". Set up a test file with the ring slot 0.008" narrower and 0.008" shorter than your desired dimension. Add multiple slots with each one 0.002" larger than the prior one. When you find the slot that fits, then you can incorporate that into your design.
I usually create several vector design files; one with each possible kerf and then I select the “right” one after I have tested my kerf. Your design is simple enough that you should be able to just tweak it on the spot based on your results.
