Using pgf, I'd like to draw an arc (part of a circle) with a given center. I don't know the exact co-ordinates of the center, because it was obtained as an intersection of other geometric objects. The desired center has a name, but no known co-ordinates. How can I do this?

Basically, I'd like to modify an instruction of the form

```
 \node (H) [name path=H, draw, circle through=(A')] at (E) {}; 

```

to produce just a part of the circle.