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Yes very similar Rick and probably easier to rotate than my method of using a Centring Circle. Still find the additional nodes created by Combine Shapes / Etc annoying.

However as I said earlier all these Combine / Arrange shapes can lead to unwanted nodes, one above another, so it's a matter of selecting the Shape Tool and Tab or Shift Tab deleting nodes (just the...

Finally select the next inner circle. Bring to front (Ctrl+F) then shift select the newly created shape. Ctrl+2 (Subtract Shapes):

Select the next outer circle (NOT the centring circle) Bring to front (Ctrl+F) then shift select the newly created shape. Ctrl+1 (Add Shapes):

Select the outer circle (NOT the centring circle) Bring to front (Ctrl+F) then shift select the newly created shape. Ctrl+3 (Intersect Shapes):

Select the eight shapes and Ctrl+1 (Add Shapes):

Select that shape & the Centring Circle. Clone. Rotate 45 degrees. Repeat a further six times:

These lines made into a shape:

Here's the lines:

Quickly.

Draw a circle over a copy of your bitmap to get it as centred as possible. Clone that circle several times and resize to match outer size, inner cog size and central hole. Clone one more...

Closest I could get Rik. I did have some issues with Ctrl+1 (Add Shapes) creating more nodes than required, needing node deletions.