The word Pierce has a specific meaning in SW, and I suspect that you are using it erroneously. That may be a problem if you are looking in SW Help.
Every Line element terminates at a Point, so I assume Splines do also. It seems to me that you want the Line terminating Point to coincide with the Circle element. This can happen only at a point on the circle element. You must define one. Your choices include a) placing a sketch Point; b) splitting the circle element which will create a Point at the split; and c) creating a Virtual Sharp. There may be others.
The mere intention that elements should coincide is not sufficient for SW. There must be points which you can Relate Coincident.
An Inference is not a Relation, it is merely a positioning based on a guess.
When sketching a line element, you can allow SW to infer Horizontal, but you will not find a Horizontal relation when you Display Relations. You must specify a Horizontal relation.
Thank you John. That was very insightful. I've made some progress over the past 24 hours with all this!