Break

Break @ Point
Break object into 2 without gap

Home Tab > Modify panel > Break at Point

Select object

Pick a point

Start Break at point command

Select the broken line

Pick a point

Repeat the command, breaking the bottom line
Switch the 2 broken lines to hidden layer

Break
Breking object into 2 with a gap

Home tab > Modify panel > Break

Select object

You need 2 points to break a gap

Command line: First point

Pick the 1st point on top

Pick 2nd point at bottom

Left portion of the circle break and delete
When break a circle, counter-clockwise rule applied

Undo the steps
Start the Break command
Select the circle
Command line: First point

Pick the 1st point at the bottom

Pick 2nd point at the top

Now it break the roght portion with gap