I have two circles that overlap, and I'm trying to remove the overlapping portion for one of the circles while keeping both of them 100% transparent.

I have something like this:



And I want this:



I accomplished the image above by making the top circle opague, but I'd like to avoid this. I've been looking at clipping, but it seems this will only remove a portion outside the clipping path, not within it. Is there a way to remove the area INSIDE the clipping path, or a different solution to accomplish the same result?

Any help is greatly appreciated, thanks!!

Select top object. Copy to clipboard.
Select both objects. Path>Division.
Delete unwanted part - it's now a separate object so just click on it to select it. Ctrl alt V to paste original in place.

Another solution, preserving the original shapes:
Set both object's fill to black and strokes to be white, group objects together (Ctrl+G),
then use the group as a masking object over a black filled rectangle (Or any other similar object).

You can use clipping to do what you want, you just need to construct the right clipping path:




Although in practice for a simple example like this I would probably just use boolean operations, per Druban's post, if you don't mind the circle being converted to a path.

Thank you so much for the suggestions! I'll try these out and see what works best. You've been a big help!