Q:

Inkscape: cutting / trimming inner line

im new to inkscape and have little to none experience with it.
i am trying to cut a circle that overlaps a line and delete the inner part of the circle, while leaving the outer part and the line?
any help appreciated!
picture below to help explain
-blue arrow indicate the line that needs to be deleted.
-red line is the cut line.
-black arrows indicate the piece to remain
-yellow arrow shows a rough drawing of what i want the finished result to be.

A:

Select the circle, then hit the "Lower Selection to bottom" button on the tool controls bar along the top, or press the keyboard shortcut End, to ensure the circle is under the irregular shape.
Copy the irregular shape using Edit > Copy or Ctrl+C
Select both shapes
From the main menu, do Path > Difference or Ctrl+-. Note that this boolean operation will consume the irregular shape. That's why it needs to be copied in step 2
Do, Edit > Paste in Place or Ctrl+Alt+V to bring back the shape that was used to cut the circle.

There's also another much simpler method. You could set the fill attribute of the upper shape to white. This method would cover part of the circle where the upper shape overlaps it.  Depending on what you are using it for, this may be a better option than the method shown above since it's non destructive.

