  Of all the distance and temporal measures in cosmology, the angular-diameter
distance, d_A(z), uniquely reaches a maximum value at some finite redshift
z_max and then decreases to zero towards the big bang. This effect has been
difficult to observe due to a lack of reliable, standard rulers, though
refinements to the identification of the compact structure in radio quasars may
have overcome this deficiency. In this Letter, we assemble a catalog of 140
such sources with 0 < z < 3 for model selection and the measurement of z_max.
In flat LCDM, we find that Omega_m= 0.24^{+0.1}_{-0.09}, fully consistent with
Planck, with z_max=1.69. Both of these values are associated with a d_A(z)
indistinguishable from that predicted by the zero active mass condition,
rho+3p=0, in terms of the total pressure p and total energy density rho of the
cosmic fluid. An expansion driven by this constraint, known as the R_h=ct
universe, has z_max=1.718, which differs from the measured value by less than
~1.6%. Indeed, the Bayes Information Criterion favours R_h=ct over flat LCDM
with a likelihood of ~81% versus 19%, suggesting that the optimized parameters
in Planck LCDM mimic the constraint p=-rho/3.
