We report the first observation of the decay B+ -> psi(3770) K+ where psi(3770) is reconstructed in the D0D0-bar and D+D- decay channels. The obtained branching fraction is Br(B+ -> psi(3770) K+)=(0.48+-0.11+-0.07)x10^{-3}. We have measured the branching fraction for the decay B+ -> D0D0-bar K+ to be (1.17+-0.21+-0.15)x10^{-3}. We have set a 90% confidence level upper limit of 0.90x10^{-3} for the decay B+ -> D+D-K+. We also present the results of a search for possible decays to DD-bar and D0D0-bar pi0 of the recently observed X(3872) particle. The analysis is based on 88 fb^{-1} of data collected at the Upsilon(4S) resonance by the Belle detector at the KEKB asymmetric-energy e+e- collider.
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