How can I delete part of an object in Inkscape?

Question

I have to delete an unwanted part of a circle object (I marked it with a blue arrow). In Ai I could have done it with the shape builder tool but in Inkscape I have no idea how to do it. The photo shows a bitmap image, on top of are basic circle shapes made with inkscape. The hen logo is based on this sketch. The bitmap won't be needed after the body of the hen is finished. (I started to follow a logo making tutorial which is originally for Adobe Illustrator, but my trial has ended so I thought I'll use Inkscape until I can purchase Ai.) Thank you for helping me.

Answer 1

You want to use path cutting operations (division, in this case). To do this, you use one shape to cut another (in this case, the gray crescent that borders the red one). One of the shapes will be destroyed during this process, so you need to copy/paste a temporary version of it.

1. Copy Ctrl+C the neighboring crescent (the large, gray one).
2. Paste Ctrl+V and align it over the original (you can do this with snapping or using Align and Distribute Ctrl+Shift+A).
3. Select the red crescent, and then select the gray one that you copied/pasted.
4. Click Path > Division or press Ctrl+/. This will break the red crescent into pieces based on how it intersected with the shape that you copied.
5. Delete the unwanted part(s) of the red crescent.

This (creating a temporary "cutting" object" to used to modify another object's path) is a fairly common way to create new and unique shapes in Inkscape. The icons in the Path menu give you a good idea of what each operation does.