Mutual Cut Line

This extension cuts exactly 2 (ideally straight) path segments and will create intersected elements. Depending on the path direction (which can be reversed) the ends are going to be cut against each other

Draw some paths

Duplicate the paths (CTRL + D) and give some different color

This step is optional but helps to understand what's going on here

Check the result

We repeat the previous step and this step for all variants to show the possible outputs. You can reverse the path using "Path → Reverse"