Answer
a) Yes
b) No
Work Step by Step
a) It does have an incenter, for all of the perpendicular bisectors of the rhombus meet at a point, and a circle centered on this point can brush the sides of the rhombus without leaving the rhombus.
b) It does not have an circumcenter, for all of the perpendicular bisectors of the rhombus meet at a point, but a circle centered on this point cannot vertices of the rhombus, for the center is not equidistant from all vertices.
