  We discuss some properties of the quantum discord based on the geometric
distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {\bf 105},
190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how
good the measure is in representing quantum discord. We explore the dependence
of quantum discord on the degree of mixedness of the bipartite states, and also
its connection with non-locality as measured by the maximum violation of a Bell
inequality within the CHSH scenario.
