How to delete part of circle path?

How do I delete part of the circle path in the picture provided?. I want the red outlined part to be deleted without having the curve change. I've tried to do this by selecting the two anchor points (where the line meets the curve and the bottom of the curve but it deletes the whole arc. I want the top arc and line connected.

Thanks.

Hi,

I'm still having trouble with this. As I said I can't place the anchor point where the line already intersects as there is already an anchor there. If I select both anchor point or either one on their own with the direct selection tool it will select the whole arc. I'm not sure exactly where I'm going wrong here. Sorry.

The 3rd picture show what happens when I select the bottom anchor with the DS tool on it's own. It will select the whole arc rather than stopping at the anchor at the intersection of the line and arc. Any ideas?

Thanks.