  The brightest blazars detected by the Fermi Gamma-ray Space Telescope Large
Area Telescope (Fermi/LAT) show significant breaks in their spectra at a few
GeV. The sharpness and the position of the breaks can be well reproduced by
absorption of $\gamma$-rays via photon--photon pair production on He ii and H i
Lyman recombination continua (LyC) produced in the broad-line region (BLR).
Using 138 weeks of LAT observations of the brightest GeV blazar 3C 454.3 we
find a power-law dependence of the peak energy on flux and discover
anti-correlation between flux and the column density of the He ii LyC which is
responsible for absorption of the >2.5 GeV photons in this object. The strength
and the variability of the absorption implies the location of the gamma-ray
emitting zone close to the boundary of the high-ionization part of the BLR and
moving away from the black hole when the flux increases. A combination of the
GeV breaks with the detection of a few powerful blazars in the TeV range puts
strong constraints on the BLR size. Additional spectral breaks at ~100 and ~400
GeV due to absorption by the Balmer and Paschen lines could be detected by the
Cherenkov Telescope Array.
