Constraints on the CKM angle γ from B ^± → Dh ^± decays using D → h ^± h′^∓ π ⁰ final states

A data sample collected with the LHCb detector corresponding to an integrated luminosity of 9 fb⁻¹ is used to measure eleven CP violation observables in B^±→ Dh^± decays, where h is either a kaon or a pion. The neutral D meson decay is reconstructed in the three-body final states: K^±π^∓π⁰; π⁺π⁻π⁰; K⁺K⁻π⁰ and the suppressed π^±K^∓π⁰ combination. The mode where a large CP asymmetry is expected, B^±→ [π^±K^∓π⁰]_DK^±, is observed with a significance greater than seven standard deviations. The ratio of the partial width of this mode relative to that of the favoured mode, B^±→ [K^±π^∓π⁰]_DK^±, is R_ADS(K) = (1.27 ± 0.16 ± 0.02) × 10⁻². Evidence for a large CP asymmetry is also seen: A_ADS(K) = −0.38 ± 0.12 ± 0.02. Constraints on the CKM angle γ are calculated from the eleven reported observables. [Figure not available: see fulltext.]