Using a compass one should be able to find the intersect at pt X. The way I did to get the arc (C). X wouldn't be a value but...
Perhaps this?...
"C" is not known though. The distance to the next hole is known but not the "plane" in which to make the hole. You can't just draw a vertical line without knowing the intersect point. Nor a horizontal line for that matter.
The way I read it was "C" is known, since it states that on your posted image. Are you referring to unknown centerlines?
Sorry, it's kind of confusing. Only the arc (C) is known but not what point on the arc to make the hole.
Friend, I like puzzles well enough, but I cannot even figure out what you are trying to figure out.
What are the constraints for where the "next hole" is supposed to be, with respect to the location of the existing hole?
Is it something like this?