Inkscape - How to cut lines across an arc?

I need to cut these lines across the arc. I only need the little itty bitty line ends. The arc and long parts of the lines are to be discarded.

Answer

Step 1

In order to use the circle to trim the line paths, you must select the circle and convert it to a path by clicking Path > Object to Path or Shift+Ctrl+C on Windows

Step 2

Select all paths except the circle and go to Path > Combine or Ctrl+K ; this allows you to perform boolean operations on the group of lines.

Step 3

Make sure the circle is above your lines with Object > Raise to Top. Then select all paths and go to Path > Cut path or Ctrl+Alt+/ This will cut the combined group along the perimeter of your circle.

Step 4

Finally, you can select each line trimming and delete them.