This forum limit only 4 images per post - so I have to split my answer into several replies.
This is one of may way of achieving what you want. For simplicity sake, I have only split the outer circle in 4.
1) Create a two circles inside each other. Make sure they are real circles :-)
Select both circles. Also note the use of guides - these are handy when dealing with stuff like this.
2) Subtract shapes by using the
Edit -> Shapes -> Subtract Shapes menu
3) Cover the bottom half + "some more" with a square. Use the guide-lines for some eye-measure. You do
NOT want to put the top of the sqaure directly on the middle of the circle.
4) Subtract the selected shapes again using the
Edit -> Shapes -> Subtract Shapes menu