  We investigate constraints on the distribution of dark matter in the
neighbourhood of the Galactic centre that may eventually be attained with the
high-resolution Event Horizon Telescope (EHT). The shadow of a black hole in
vacuum is used to generate a toy model describing how dark matter affects the
size of the shadow of the supermassive black hole located at the Galactic
centre. Observations by the EHT may constrain the properties of the dark matter
distribution in a possible density spike around the black hole. Current
uncertainties due to both the resolution of the telescope and the analysis of
stellar orbits prevent one from discerning the effect of dark matter on the
measured size of the shadow. The change in the size of the shadow induced by
dark matter can be seen as an additional uncertainty in any test of general
relativity that relies on using the angular size of the shadow to estimate the
Schwarzschild radius of the black hole.
