  We present the first determination of the intrinsic triaxial shapes and
tree-dimensional physical parameters of both dark matter (DM) and intra-cluster
medium (ICM) for the galaxy cluster Abell 1689. We exploit the novel method we
recently introduced (Morandi et al. 2010) in order to infer the
tree-dimensional physical properties in triaxial galaxy clusters by combining
jointly X-ray and strong lensing data. We find that Abell 1689 can be modeled
as a triaxial galaxy cluster with DM halo axial ratios 1.24 +/- 0.13 and 2.37
+/- 0.11 on the plane of the sky and along the line of sight, respectively. We
show that accounting for the three-dimensional geometry allows to solve the
discrepancy between the mass determined from X-ray and strong gravitational
lensing observations. We also determined the inner slope of the DM density
profile alpha: we measure alpha = 0.90 +/- 0.05 by accounting explicitly for
the 3D structure for this cluster, a value which is close to the cold dark
matter (CDM) predictions, while the standard spherical modeling leads to the
biased value alpha = 1.16 +/- 0.04. Our findings dispel the potential
inconsistencies arisen in the literature between the predictions of the CDM
scenario and the observations, providing further evidences that support the CDM
scenario.
