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Radio pulsars exhibit several unexplained phenomena, in particular the average pulse profiles with the apparent core-cone structure and interesting frequency evolution. I show that they can be interpreted through essential geometric properties of the inverse Compton scattering. If the scattering occurs in a dipolar magnetosphere and the mean-free-path is long, a nested cone structure is expected with the cone size ratio of two-thirds, which is consistent with observations. Being a discontinuous process, the scattering is consistent with the discrete altitude structure of emission rings as derived from aberration-retardation effects. Assuming that the upscattered signal is the curvature radiation (CR), one can interpret the observed bifurcated components (BCs) as a magnified microbeam of CR: the BCs are wide low-frequency CR microbeams that have been upshifted in frequency with their width preserved by beam-copying scattering in divergent magnetic field. The large flux of BCs is partly caused by compression of the full emitted spectrum into the narrow observed bandwidth, which explains why the frequency-resolved BCs have the frequency-integrated shape. The wide low-frequency microbeams can encompass large magnetospheric volumes, which considerably abates the requirements of the energy needed for coherency. The properties of BCs thus suggest that the observed modulated radio flux is strongly affected by the scattering-driven blueshift and spectral compression. The relativistic beaming formula (1/γ) is not always applicable, in the sense that it may not be directly applied to some blueshifted profile features.