I'd try making a 'C' shape that is about as wide as the ring you want. The with the filter set for 'Documentation' select the outer edge and RMB>Pull arc, then select the inner edge and repeat. Once you have the shape massaged to fit as you want for 1/2 of your ring, copy and mirror it for the other half.
Best of luck-
Two C shapes is the right approach, and it's easy once you know how.
If you need complete accuracy, draw two circles as guidelines first, for the inner and outer diameters of the ring. But eyeballing works too.
Draw the 1st keepout using polygon mode as a block V, with the top of the two legs the width of the keepout, and the bottom vertices on the bottom quadrants of the circles. That's just 6 sides and 6 vertices. Set it to the keepout conditions you need.
Now, select the outer bottom vertex, right click, and select Pull Arc. Boom, instant half circle. Place it as you need it.
Repeat for the inner diameter. Copy and mirror or rotate the shape for the other half-circle.