I have a circle, an ellipse, and two lines connecting them.  The ends of the lines have been snapped to tangential nodes.  How can I trim away the parts of the circle and ellipse at the tangential nodes? I've drawn Xs over those parts of the circle and ellipse to show what I want to cutaway.  In a CAD tool this would be done with a Trim tool.  How do you do this in Inkscape 1.2.

Maybe this:

Thanks to @krausest for the Subject Trim? Had been playing with similar item aka gasket. Had no problem in FreeCad. Six circles, four lines and constraints, then trim. Print out life size to cut in gasket paper. When I saw Trim? knew what it was about.  😀

Two thanks to @TylerDurden One for where he told me how to change the snap indicator size so I can see it and the other for this method. 😀

Thanks.  Draw a line connecting the tangential nodes, select the 1) line and the 2) circle.  Then Cut Path and delete the objects that have been cut into separate objects.  Thanks.