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The ratio between the branching fractions of the B 0 → ρ (770) 0 γ and B 0 → K * (892) 0 γ decays is measured with proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb − 1 . The measured value is B B 0 → ρ 770 0 γ B B 0 → K ∗ 892 0 γ = 0.0189 ± 0.0007 ± 0.0005 , where the first uncertainty is statistical and the second systematic. The branching fraction for B 0 → ρ (770) 0 γ decays is hence obtained as B B 0 → ρ 770 0 γ = 7.9 ± 0.3 ± 0.2 ± 0.2 × 10 − 7 , where the last uncertainty is due to the branching fraction of the normalisation mode. This result assumes that both the ρ (770) 0 and K * (892) 0 decays saturate the dihadron mass spectra considered in the analysis. It is consistent with the current world-average value and by far the most precise measurement to date.