  We find a single parameter family of genuinely entangled three qubit pure
states, called the maximally Bell inequality violating states (MBV), which
exhibit maximum Bell inequality violation by the reduced bipartite system for a
fixed amount of genuine tripartite entanglement quantified by the so called
tangle measure. This in turn implies that there holds a complementary relation
between the Bell inequality violation by the reduced bipartite systems and the
tangle present in the three qubit states, not necessarily pure. The MBV states
also exhibit maximum Bell inequality violation by the reduced bipartite systems
of the three qubit pure states with a fixed amount of genuine tripartite
correlation quantified by the generalized geometric measure, a genuine
entanglement measure of multiparty pure states, and the discord monogamy score,
a multipartite quantum correlation measure from information theoretic paradigm.
The aforementioned complementary relation has also been established for three
qubit pure states for the generalized geometric measure and the discord
monogamy score respectively. The complementarity between the Bell inequality
violation by the reduced bipartite systems and the genuine tripartite
correlation suggests that the Bell inequality violation in the reduced two
qubit system comes at the cost of the total tripartite correlation present in
the entire system.
