or explode all the circles 1 time to Polyline and the Trim Object work.
Just adding a note for any new users who may read this. Exploding Circle, Arc, spline, or Bezier creates a polyline, which consists of lots of small line segments to represent the curvature. This can cause problems further down the line. i.e. Radius and Diameter dimension won't work, and Extrude / Loft will have lots of flat edges and can cause 3d filleting (blending) not to work. That said there are circumstances where exploding circles will not harm the drawing, and may be beneficial.
Ed. Whilst Torfinn has provided the solution. I'd thought I'd just mention what I do. Rather than trim lines, circles and arcs for an extrusion / loft. I use the Polyline tool. On an object like yours, I'd turn on Snaps, and just intersection and magnetic point. I would switch the polyline to use arcs segments (right click or inspection bar). and just snap at each intersect point.
If everything id drawn perfectly like your is, there is no need to change to line segments as TC will do that automatically for the straight sections. And near the end, just before reaching the start point again, I right click and choose close. Thus, ensuring a fully closed profile for extrusion. Snapping a polyline is often much quicker for me, than trimming things. but, this fails if the original arcs / lines are not drawn accurately to start with.
Just my thoughts.