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With Hubble Space Telescope Fine Guidance Sensor 3 we have determined a parallax for the white dwarf–M dwarf interacting binary, Feige 24. The white dwarf (DA) component has an effective temperature Teff ~ 56,000 K. A weighted average with past parallax determinations (πabs = 14.6 ± 0.4 mas) narrows the range of possible radius values, compared with past estimates. We obtain RDA = 0.0185 ± 0.0008 R with uncertainty in the temperature and bolometric correction the dominant contributors to the error. Fine Guidance Sensor 3 photometry provides a light curve entirely consistent with reflection effects. A recently refined model mass-luminosity relation for low-mass stars provides a mass estimate for the M dwarf companion, MdM = 0.37 ± 0.20 M, where the mass range is due to metallicity and age uncertainties. Radial velocities from Vennes and Thorstensen provide a mass ratio from which we obtain MDA = 0.49 M. Independently, our radius and recent log g determinations yield 0.44 M < MDA < 0.47 M. In each case, the minimum DA mass is that derived by Vennes & Thorstensen from their radial velocities and Keplerian circular orbits with i ≤ 90°. Locating Feige 24 on an (M, R)-plane suggests a carbon core. Our radius and these mass estimates yield a value of γgrav inconsistent with that derived by Vennes & Thorstensen. We speculate on the nature of a third component whose existence would resolve the discrepancy.