We present a strong-lensing analysis of the galaxy cluster MACS J1206.2-0847 ($z$=0.44) using UV, Optical, and IR, HST/ACS/WFC3 data taken as part of the CLASH multi-cycle treasury program, with VLT/VIMOS spectroscopy for some of the multiply-lensed arcs. The CLASH observations, combined with our mass-model, allow us to identify 47 new multiply-lensed images of 12 distant sources. These images, along with the previously known arc, span the redshift range $1la zla5.5$, and thus enable us to derive a detailed mass distribution and to accurately constrain, for the first time, the inner mass-profile of this cluster. We find an inner profile slope of $dlog Sigma/dlog thetasimeq -0.55pm 0.1$ (in the range [1arcsec, 53arcsec], or $5la r la300$ kpc), as commonly found for relaxed and well-concentrated clusters. Using the many systems uncovered here we derive credible critical curves and Einstein radii for different source redshifts. For a source at $z_{s}simeq2.5$, the critical curve encloses a large area with an effective Einstein radius of $theta_{E}=28pm3arcsec$, and a projected mass of $1.34pm0.15times10^{14} M_{odot}$. From the current understanding of structure formation in concordance cosmology, these values are relatively high for clusters at $zsim0.5$, so that detailed studies of the inner mass distribution of clusters such as MACS J1206.2-0847 can provide stringent tests of the $Lambda$CDM paradigm.
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