We report on a search for charmless hadronic B decays to the three-body final states K0Sh+-pi-+, K+-h-+pi0, and K0Sh+-pi0 (h+- denotes a charged pion or kaon), using 9.12 fb-1 of integrated luminosity produced at sqrt{s}=10.58 GeV and collected with the CLEO detector.We observe the decay B -> K0pi+pi- with a branching fraction (50+10-9+-7)x10-6 and the decay B -> K*(892)+-pi-+ with a branching fraction (16+6-5+-2)x10-6, where the uncertainties are statistical and systematic, respectively.Both branching fractions are averages over CP-conjugate states. We also search for a CP-violating asymmetry in the decay B -> K*(892)+-pi-+.We find ACP(B -> K*(892)+-pi-+)=0.26+0.33-0.34+0.10-0.08, giving an allowed interval of [-0.31,0.78] at the 90% confidence level. These measurements are used to constrain fundamental parameters of the Standard Model.
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Observation of B -> K^0_S pi^+ pi^- and B -> K^*(892) ^+- pi^-+ and measurement of the charge asymmetry in B -> K^*(892)^+- pi^-+