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-+/-pi(-/+)pi(0); pi(+)pi(-)pi(0); K+ K- pi(0) and the suppressed pi K-+(-/+)pi(0) combination. The mode where a large CP asymmetry is expected, B-+/- -> [K-+/-pi(-/+)pi(0)] K-D(+/-), 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-+/-pi(-/+)pi(0)] K-D(+/-), is R-ADS(K) = (1.27 +/- 0.16 +/- 0.02) x 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 gamma are calculated from the eleven reported observables.