Constraints on the CKM angle γ from B± → Dh± decays using D → h±h′∓π0 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 RADS(K) = (1.27 ± 0.16 ± 0.02) × 10−2. Evidence for a large CP asymmetry is also seen: AADS(K) = −0.38 ± 0.12 ± 0.02. Constraints on the CKM angle γ are calculated from the eleven reported observables.