Possibly?.....Select all > Offset path > Divide (Pathfinder Palette) > Ungroup - and then delete all the appropriate "inbetween" parts?
What Joe said with the addition that Offset Path may be used before or after Divide, without deleting anything; you may Object>Ungroup or keep them grouped.
If you wish to have plain shapes, you may Object>Expand Appearance and Object>Ungroup (twice and then Object>Group if you want to keep them grouped).
Can't get this to work at all.
Been trying it out with a much simpler image (screenshot at the bottom):
I'd like to use the two big rectangles and the diagonal line in the center of the small circle to CUT OFF
from the 3 circle shapes in the middle of the image.
The result should give me 3 arcs on both the left and the right side that I can fill with different colors.
Should be easy as pie, but somehow the methods suggested to me above (thanks, guys) doesn't work for me.
What am I doing wrong?
Your screenshot does not tell anyone what you have.
Your three "rings" could be:
Simple paths with heavy strokes applied.
Simple filled paths, with white filled paths stacked between them.
Which are they?
They are actually just 3 circles created with the Ellipse Tool and then adjusted with a heavy blue stroke.
And I think that's the problem. I'm playing around with it right now, creating circles and joining them into shapes instead... maybe it'll help.
You're welcome to post ideas and solutions in the meanwhile, of course.
1. Black Pointer: Select the three circles. Object>Path>Outline Stroke. Now each ring is a filled compound path. You have three compound paths, each with two subpaths.
2. Black Pointer: Select the diagonal path. Object>Path>Outline Stroke. Now it is a a simple filled path.
3. Black Pointer: Select the small ring and the diagonal path. Pathfinder Palette: Click the Subtract... button. The diagonal rectangle "punches" the ring, like a cookie-cutter. The former ring is now a group of two simple closed paths.
4. Black Pointer: Select the two large rectangles. Object>Compound Path>Make. Now the two rectangles are subpaths of a compound path. This is so the two rectangles will act as one object in step 6.
5. Black Pointer: Select the two large rings, Object>CompoundPath>Make. Now the two rings are one compound path with four subpaths. This is so the rings will act like one object in step 6.
6. Black Pointer: Select the rectangles (one compound path) and the large rings (another compound path). Pathfinder Palette: Click the Subtract... button. The semicircles are now a Group containing four simple paths.
The above assumes you are using CS4 on Windows. If you are using CS3 or earlier, press and hold Alt each time you are instructed to click the Pathfinder button. If you are using Mac OS, it's the Option key, not Alt (I think).
When using the Subtract... Pathfinder button, the object in front does the cutting; the object below gets cut.
The new task is quite different from the original one.
If the three circles and the slanting line consist of simple unfilled (wide) strokes, you may select all and:
0) Object>Path>Outline Stroke;
Then you should have filled Paths, three of them Compound, and you may, if/when the slanting rectangle is on top of the inner circle:
1) Select the inner circle and the line and Pathfinder>Minus Front (Subtract from shape area, hold Alt/Option if needed to expand to get simple paths);
2) Select the rectangles and the two outer circles and Pathfinder>Minus Front (etc).
Edit: delayed by a magpie.
I worked out this one just fine. Cool. Still getting the hand of manipulating and combining shapes and paths. It's tricky for a newb.
For my part you are welcome, ufoldager.
I can't seem to get the magpie excuse to work for me. Could you please explain how to do it?