I do not do a lot of drawing annotations automation, but I may be able to help a bit. Are you using the Inventor API tools for drawing dimension creation, or the uniquely iLogic API tools? In both situations, one of the 'Optional' inputs that the GeometryIntent creation method asks for is a variation of the PointIntentEnum. There are variations of that Enum specifically for specifying common points in circular scenarios (as well as rectangular, axial, and planar) which should work, as long as the drawing curve geometry supports that Enum variation. Then, the iLogic API methods allow us to specify yet another optional helper called a CurveChoiceSpec. It's description is: "If more than one drawing curve is found, chooses the one whose bounding box center is closest to this point." It uses a DocumentUnitsPoint2d type object for the actual location. Those can be created using the IManagedDrawingView.SheetPoint Method, or the ThisDoc.Geometry.Point2D Method.
Methods for Creating GeometryIntent:
Sheet.CreateGeometryIntent (Inventor API method)
IManagedDrawingView.GetIntent Method (String, PointIntentEnum, CurveChoiceSpec) (iLogic API method)
IManagedDrawingView.GetIntent Method (ComponentArgument, String, PointIntentEnum, CurveChoiceSpec) (iLogic API method)
GeneralDimension creation methods source objects:
GeneralDimensions (Inventor API object)
IManagedGeneralDimensions Interface (iLogic API object)
Wesley Crihfield

(Not an Autodesk Employee)