I though I was following all this until your last post. If the "centerline" goes through the circle but not its center, what kind of centerline is it, how was it constructed and what is it related to?
It does sound like you may be into an issue of what mathematical "space" each of these entities exist in. it may not be logical for the program to handlea relationship between them.
If you centerline is, say a large one on a large dismaeter circle (a big dashed cross) and it happens to pass through, say another circle, I don't think you can do what you want. Those types of "center marks" are more of a fonted symbol be nature rather than true geometry as such. They have few, if any identifiable locations on them (I think just the center).
3/4 of all the Spam produced goes to Hawaii - shame that's not true of SPAM also.......