How to cut intersecting paths in illustrator

Question

This is quite a simple question ( I would assume) but I am not able to figure how to do this.

I have 2 circular paths without any fill inside. Looks like this

I want to cut it so the paths are like this

I have used the scissors tool to give an example here, but I am sure there is a better way. Not able to find anything in the pathfinder window I don't like using clipping masks because all it does (IMO) is it gives an illusion that things have been clipped. But the shape remains, only a part of it remains invisible. Correct me if I am wrong

How do I do this? I don't want to hide any part of the path on top of the other. I want to cut the paths properly.

Answer 1

Use the Shape Builder Tool.

Select both circles and merely drag across the path you don't want.

Answer 2

This is just to answer OP's question of other ways of achieving the same result. The best way to do this is still using the Shape Builder tool as mentioned by Metis.

Another Way

1. Create two intersecting circles
2. Select both
3. Go to Window > Pathfinder
4. Select the Divide option.

Now this will create anchor points on the intersecting joints. Ungroup the generated vector and delete the extra intersection (as there are two objects, there will be two outline strokes. This is to remove the extra one)

Now select the Direct Selection Tool and click on the right circle (for this particular case)

You will notice an anchor point in the middle of the inside curve (refer to the screenshots below). Delete that and the desired result would be achieved.

(Excuse the non-alignment)

Answer 3

You can use Pathfinder. It's fast and it works in any other vector editor (Sketch, Figma, you name it).

1. Select one of the circles. Copy-paste it above the original. Use Paste in front command to paste the circle right over the original one.

2. Select the second circle and use subtract tool in the Pathfinder palette

3. Voila!