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Recently, many unexpected new particles were discovered with masses around 4 GeV/c2. They are collectively called XYΖ mesons and while some of them have been identified as charmonium states, many others have properties that don't fit into the quark-antiquark classification, and so far remain unclassified. The X(3872) meson was the first to be discovered and is the most studied of these states, and there is a variety of hypotheses on its nature. Other new states include the X(3940) and Y (3940) mesons, which have the same mass and similar widths; it is not clear if they are the same state or not. More experimental evidence is required to understand these particles. We report a search for B → X(3872)K with X(3872) decaying to D*0 D0 using a sample of 657 million BB pairs recorded at the γ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. The study is performed for both D*0 → D0γ and D*0 → D0π0 decay modes. We find a total signal of 50.1 events with a mass of 3872.9 MeV/c2, a width of 3.9 MeV/c2 and a product branching fraction Ɓ(B→ X(3872)Κ) × Ɓ(X(3872) → D*0 D0) = (0.80 ± 0.20 ± 0.11) × 10-4. The statistical significance of the signal is 7.9σ. Furthermore, from the same study we also set an upper limit at 90% confidence level on the product branching fraction Ɓ(B→ Y(3940)K) × Ɓ(Y (3940) → D*0 D0) < 0.67 × 10-4 which suggests that the X(3940) and Y (3940) mesons are different states.