That's a frequent question, Frank. A datum doesn't automatically have a center, much less a reproducible one. If the radius was more than 180-deg, it would have a reproducible center. Unfortunately, the '94 and preceding standards, while allowing mathematically defined datum features, don't in any that I can recall show you how to use them. Thus the recurring questions of "where's the center" and "where do I measure from". '09 improved on things a bit by allowing MMB and LMB modifiers to non-features of size, as well as BSC and [stated values].
In the figure CH posted, what is the relationship between the radii segments? There are 4 of them that need to be related back to each other or to datums A/B/C. There is an IMPLIED coaxiality of the features, but no control provided. If they were FOSs, then position could be used. For better or for worse, the only geometric control that locates surfaces is Profile of a Surface. As the radial "size" dimension is based on a center point (i.e. center location), it must be repeatable to have any kind of functional meaning. By the Principle of Simultaneous Requirements, if the two outer radii (R9 & R11) were controlled with a profile of .02/A/B/C, and the two inner radii (R9.938 & R10.062) were controlled with a profile of .01/A/B/C, then they would all be gauged/inspected together, making the actual center irrelevant. That would, however, establish legitimate controls for the implied condition that I read into the drawing. The datum feature simulator for radius segment datum feature B, establishing Datum B, is of "perfect form & size" within gaugemaker tolerances, and therefore it can be used to establish a center that would be used to locate the four holes controlled with position.
From a Y14.5 perspective, this drawing is rather poor. Some controls are evidently missing, and the two surface profiles (2 SURFACES on each) should be wrt the DRF as well.
Jim Sykes, P.Eng, GDTP-S
Profile Services
TecEase, Inc.