  For any real pair i, j geq 0 with i+j=1 let Bad(i, j) denote the set of (i,
j)-badly approximable pairs. That is, Bad(i, j) consists of irrational vectors
x:=(x_1, x_2) in R^2 for which there exists a positive constant c(x) such that
max {||qx_1||^(-i), ||qx_2||^(-j)} > c(x)/q for all q in N. A new
characterization of the set Bad(i, j) in terms of `well-approximable' vectors
in the area of 'twisted' inhomogeneous Diophantine approximation is
established. In addition, it is shown that Bad^x(i, j), the `twisted'
inhomogeneous analogue of Bad(i, j), has full Hausdorff dimension 2 when x is
chosen from the set Bad(i, j). The main results naturally generalise the
i=j=1/2 work of Kurzweil.
