  We study a special class of non-convex quadratic programs subject to two
(possibly indefinite) quadratic constraints when the level sets of the
constraint functions are {\it not} arranged {\it alternatively.} It is shown in
the paper that this class of problems admit strong duality following a tight
SDP relaxation, without assuming primal or dual Slater conditions. Our results
cover Ye and Zhang's development in 2003 and the generalized trust region
subproblems (GTRS) as special cases. Through the novel geometric view and some
simple examples, we can explain why the problem becomes very hard when the
level sets of the constraints are indeed arranged alternatively.
