  For the case of Tycho's supernova remnant (SNR) we present the relation
between the blast wave and contact discontinuity radii calculated within the
nonlinear kinetic theory of cosmic ray (CR) acceleration in SNRs. It is
demonstrated that these radii are confirmed by recently published Chandra
measurements which show that the observed contact discontinuity radius is so
close to the shock radius that it can only be explained by efficient CR
acceleration which in turn makes the medium more compressible. Together with
the recently determined new value $E_{sn}=1.2\times 10^{51}$ erg of the SN
explosion energy this also confirms our previous conclusion that a TeV
gamma-ray flux of $(2-5)\times 10^{-13}$ erg/(cm$^2$s) is to be expected from
Tycho's SNR. Chandra measurements and the HEGRA upper limit of the TeV
gamma-ray flux together limit the source distance $d$ to $3.3\leq d\leq 4$ kpc.
