So I am trying to add supports to my model for 3D printing. I have extruded some circles up to the model, and then cut extruded a small gap between them and the model as you can see in the picture. I want to make sharp tips on the tops of these so I can break my model off easily when it finishes printing.

I thought I could just click on the face of the supports where I cut extruded through (the black part) and it would just make a tangent plane that I could build the tips from, but it doesn't appear to be that easy. Can someone please tell me how I would go about making conical tips on the supports that point towards the centre of the model (the model is circular)?