Mesh point using circle center does not work.
Solution
Mesh point at the center point of a arc is intended for holes. So that an RBE3 can be created from the center of a hole to an edge. The 2D mesher will not use mesh points created at the center of an arc. The resulting point is associated to the edge. Either point or mesh point can be used for this (spider from cp to arc).
For the case were there happens to be a face at the center of the arc, since the point is associated to the edge and not the face, the mesher does not find any points on the face when asking the point system for points on the face. The point system does not return the point to the mesher when meshing the edge either because it knows the type of point on the edge is center of arc.
The point system does not support dual geometry association to both the edge and a face.
To get the point at the circle center use following
"Insert" -> "Model Preparation" -> "Mesh Point" -> Type to Project.
Object to Project to -> Select the Surface.
Point -> Circle Center.
Notes