1. Create a 163 x 163 px canvas.
2. View > Create new guide at 1, 81.5, and 162, both V and H.
3. Turn on Snap to Guides; turn off other snaps.
4. Set the zoom level high (I used 500%) so the grid almost fills the screen.
5. Use the ellipse tool, with "path" button selected in the options bar, to draw a circle; click and hold at the center point, then drag with alt+shift depressed, until the circle touches the outer guides (and the info screen shows W and H to be 161).
6. Save this path with the name 161px.
7. Copy the path; name it 159px.
8. Select 159px in the paths pallette; then click on the path with the path selection tool.
9. Image > Path Transform > Scale; in the H and W boxes, enter 159px and click the checkmark.
10. Right click on the 161px path, pick Make Selection; 0px feathering, antialias on. 11. Fill the selection with black (or whatever color you want) using the paint bucket. 12. Ctrl+D to delete selection; now make selection from the 159px path. Press delete to empty the middle. Ctrl+D to delete selection.
13. If desired, change the canvas size to 161 x 161 px, centered.
You now have an aliased circle that is precisely centered within a 161 x 161 px area, goes to its edges, and does not go beyond.
If you don’t want it aliased, then turn antialiased off when making selections in steps 10 and 12. If you want it filled, ignore step 12 (and don’t bother with creating the 159px path.
You can take a look at the result here <
http://www.camsul.com/161px-circle.png>.