  We typically measure the radii of transiting exoplanets from the transit
depth, which is given by the ratio of cross-sectional areas of the planet and
star. However, if a star has dark starspots (or bright regions) distributed
throughout the transit chord, the transit depth will be biased towards smaller
(larger) values, and thus the inferred planet radius will be smaller (larger)
if unaccounted for. We reparameterize the transit light curve to account for
"self-contamination" by photospheric inhomogeneities by splitting the parameter
$R_p/R_\star$ into two parameters: one for the radius ratio -- which controls
the duration of ingress and egress -- and another which measures the possibly
contaminated transit depth. We show that this is equivalent to the formulation
for contamination by a second star (with positive or negative flux), and that
it is sensitive to time-steady inhomogeneity of the stellar photosphere. We use
synthetic light curves of spotted stars at high signal-to-noise to show that
the radius recovered from measurement of the ingress/egress duration can
recover the true radii of planets transiting spotted stars with axisymmetric
spot distributions if the limb-darkening parameters are precisely known. We fit
time-averaged high signal-to-noise transit light curves from Kepler and Spitzer
of ten planets to measure the planet radii and search for evidence of spot
distributions. We find that this sample has a range of measured depths and
ingress durations which are self-consistent, providing no strong evidence for
contamination by spots. However, there is suggestive evidence for occultation
of starspots on Kepler-17, and that relatively bright regions are occulted by
the planets of Kepler-412 and HD 80606. Future observations with the James Webb
Space Telescope may enable this technique to yield accurate planetary radii in
the presence of stellar inhomogeneities.
