I'm trying to draw a plasmid DNA with "sticky ends," which are just the zig-zaggy ends of an arc as seen below.



I'm only trying to draw something similar to the image on the right, but with only one color on the arcs and no black outlines. So all I need is just a stroked circle and white-stroked zig-zaggy paths on top. The problem is creating those paths.

I've tried creating the three little pieces (2 lines, 1 arc) but I had a hard time getting nodes to snap together. Then I tried create the three pieces that are longer than I need and than having them cut each other to size (literally with the "cut" operation), but with little success. For example, when I cut one of the radial lines with an arc, instead of getting two lines, I only got one, and usually not the one I want (see attachment). Somehow I managed to got the top line as a I want, but when I tried to do the bottom one, I only kept getting the inner half, whereas the outer half disappeared. Hope this makes sense.

So can you explain to me how I can use the boolean operations to do what I want? Or snap? Or any other methods to achieve my (sticky) ends? Thank you so much.

You can use a grid, and bezier tool do draw the zigs.



These are white zigs on a white background. You could cut them into the ring with a boolean difference.

Hi.

Boolean operations work on the enclosed area of the paths. By your paths are open and have only two nodes with a straight segment, it doesn't work.
There are many possible solutions to draw something alike.
Keep in mind that inkscape has a transparent background by default, and, even if you set it to an opaque colour, it won't be seen in a browser.
If you want to add white zig-zags atop, that go over the edge of the circle, it will be seen if you don't draw a white background -for example draw a white rectangle and move it to the bottom (End).
As suggested above, the pen tool can give you the fastest workaround. Instead of drawing three different paths, draw one with 4 segments.
You can draw over the existing objects, with the snapping to path intersections enabled.

To cut the zig-zags out, both objects should be represented by closed paths, with fill and no outline.
Probably your circle has only 4 nodes, instead of being a ring with 8 nodes; so for the boolean, convert both object's stroke to path (Ctrl+Alt+C).