Select the diagonal line and the circle. From the Arrange menu, select
Combine Shapes > Slice Shapes (or use the keyboard shortcut Ctrl 4).
Select the small ellipse and the right half of the sliced circle and
Arrange > Combine Shapes > Add Shapes or press Ctrl 1. This creates
the combined shape shown in the green outline.
Select the horizontal ellipse and from the Arrange menu, select
Convert to Editable Shapes. With the horizontal ellipse still selected,
switch to the Shape Editor Tool (F4). Drag a selection rectangle that
passes over the two middle control points, which when highlighted have
red outlines.
On the Infobar at the top of the screen, press the Break at Points icon.
Switch back to the Selector Tool F2 (the arrow pointer), select the rear
portion of the ellipse (shown in blue dashed outline) and delete it.
Select the remaining half of the sliced horizontal ellipse and then green
outlined shape and Arrange > Combine Shapes > Slice Shapes (Ctrl 4).
The front portion of the horizontal ellipse goes away and the green
shape is now divided into two parts.
Select the ellipse shown in black outline and copy it to the clipboard
(Ctrl c or Edit > Copy).