How to cut intersecting paths in illustrator

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
enter image description here

I want to cut it so the paths are like this
enter image description here

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

Use the Shape Builder Tool.

Select both circles and merely drag across the path you don’t want.
enter image description here

Attribution
Source : Link , Question Author : Dhaval Shukla , Answer Author : Scott

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