In this paper, we propose a new approach to determining cosmological distances to active Galactic nuclei (AGNs) via light travel-time arguments, which can be extended from nearby sources to very high redshift sources. The key assumption is that the variability seen in AGNs is constrained by the speed of light and therefore provides an estimate of the linear size of an emitting region. This can then be compared with the angular size measured with very long baseline interferometryer to derive a distance. We demonstrate this approach on a specific well-studied low-redshift (z = 0.0178) source 3C 84 (NGC 1275), which is the bright radio core of the Perseus Cluster. We derive an angular diameter distance including statistical errors of DA = 72+5？6 Mpc for this source, which is consistent with other distance measurements at this redshift. Possible sources of systematic errors and ways to correct for them are discussed.