Two analyses are performed using data collected by the LHCb experiment during 2011. Both consider decays of charged B mesons reconstructed in the π±μ+μ− final state. Decays involving dimuons provide an experimentally clean signature, even in the high-background environment of the √s = 7 TeV proton-proton collisions at the LHC. The first analysis measures the CP asymmetry of B±→Ψπ± decays using 0.37 fb-1 of data, where the dimuon decays of two resonances are considered, J/ψ→μ+μ− and ψ(2S)→μ+μ−. The branching fraction is measured relative to the Cabibbo favoured B±→ΨK± mode. The second analysis uses 1 fb-1 of data to make the first observation of the non-resonant B±→π±μ+μ− decay. The branching fraction is measured relative to that of B±→K±μ+μ−, and measurements of the CP asymmetry and the ratio of CKM matrix elements Vtd/Vts are obtained. The branching fractions of the decays of interest are found to be B(B±→J/ψ π±) = (3.88 ± 0.11 ± 0.15) x 10-5, B(B±→ψ(2S) π±) = (2.52 ± 0.26 ± 0.15) x 10-5 and B(B±→π±μ+μ−) = (2.48 + 0.57 −0.52 ± 0.17) x 10-8, where the first uncertainty is related to the statistical size of the sample and the second quantifies systematic effects. The measured CP asymmetries in these modes are A CP (J/ψ π) = 0.005 ± 0.027 ± 0.011, A CP (ψ(2S) π) = 0.048 ± 0.090 ± 0.011 and A CP (μμπ) = -0.045 ± 0.220 ± 0.066, with no evidence of direct CP violation seen. The ratio of matrix elements is measured as Vtd/Vts = 0.274 + 0.031 − 0.028 ± 0.008, which is in agreement with previous results.