Topics created by orchidacaea

If the edges are all coplanar then something like http://sketchucation.com/pluginstore?pln=addfaces
should work, if all edges are selected and the plugin is then run...

Draw an arc?
Screenshot - 1_8_2015 , 4_20_29 AM.png

I don't know if you want them but you can get smoother curves all the way around if you increase the number of sides on the circle and the circle you used to create the half-ellipse.
Screenshot - 1_8_2015 , 4_27_36 AM.png

Geometry drawn in the same context immediately 'merges', so the circles will cut each other.
This is useful to do what Pilou shows, but a PIA when you want to Move one circle as drawn over the other. e.g. if you have not initially drawn it in the exact position you desire.
To allow that, draw the second circle away from everything else, then select it and use the context-menu to make it into a [temporary] group.
Now you can select the temporary group and Move it etc, sliding it over the other circle to adjust the overlapping.
When you are ready explode the temporary group.
The circles will merge and cut each other as before...
Erase the unwanted parts...

In addition to what @pbacot suggests, this is an operation where you may run into SketchUp's well-known issue with very small Faces. You may have to scale your objects up, do the operation, and then scale them back down to avoid creating holes or gaps.