Trying to make a logo similar to this in Inkscape but cannot get the parts of the circle to cut out around the image. I've tried everything. Difference, intersection, Object-Set-Cut. Nothing works. The image I am using in place of the bicycle is also ungrounded.
There are several ways to do it. Here are some:
One method is to copy and paste several circles in place, then edit the start and end points of the arcs.
Another method is to use a clipping path. First create a shape on top of the circle, then select both circle and shape, and do Object > Clip > Set
Another is to give your text/artwork a thick outer white stroke so that it hides parts of the circle behind the stroke.