  We investigate isotropic-isotropic, isotropic-nematic and nematic-nematic
phase coexistence in binary mixtures of circular platelets with vanishing
thickness, continuous rotational degrees of freedom and radial size ratios
$\lambda$ up to 5. A fundamental measure density functional theory, previously
used for the one-component model, is proposed and results are compared against
those from Onsager theory as a benchmark. For $\lambda \leq 1.7$ the system
displays isotropic-nematic phase coexistence with a widening of the biphasic
region for increasing values of $\lambda$. For size ratios $\lambda \geq 2$, we
find demixing into two nematic states becomes stable and an
isotropic-nematic-nematic triple point can occur. Fundamental measure theory
gives a smaller isotropic-nematic biphasic region than Onsager theory and
locates the transition at lower densities. Furthermore, nematic-nematic
demixing occurs over a larger range of compositions at a given value of
$\lambda$ than found in Onsager theory. Both theories predict the same
topologies of the phase diagrams. The partial nematic order parameters vary
strongly with composition and indicate that the larger particles are more
strongly ordered than the smaller particles.
