  We analyze the Coulomb breakup cross sections of $^{11}$Li and $^6$He nuclei
using a three-body model with a density-dependent contact interaction. We show
that the concentration of the B(E1) strength near the threshold can be well
reproduced with this model. With the help of the calculated B(E1) value, we
extract the root-mean-square (rms) distance between the core nucleus and the
center of mass of two valence neutrons without resorting to the sum rule, which
may suffer from unphysical Pauli forbidden transitions. Together with the
empirical rms distance between the neutrons obtained from the matter radius
study and also from the three-body correlation study in the break-up reaction,
we convert these rms distances to the mean opening angle between the valence
neutrons from the core nucleus. We find that the obtained mean opening angles
in $^{11}$Li and $^6$He agree with the three-body model predictions.
