We consider light scattering by two dimensional arrays of high-index
dielectric spheres arranged into the triangular lattice. It is demonstrated
that in the case a triple degeneracy of resonant leaky modes in the Gamma-point
the scattering spectra exhibit a complicated picture of Fano resonances with
extremely narrow line-width. The Fan features are explained through coupled
mode theory for a Dirac cone spectrum as a signature of optical bound states in
the continuum (BIC). It is found that the standing wave in-Gamma BIC induces a
ring of off-Gamma BICs due to different scaling laws for real and imaginary
parts of the resonant eigenfrequencies in the Dirac cone spectrum. A
quantitative theory of the spectra is proposed
