We present a study of $Bto X(3872)K$ with X(3872) decaying to $D^{*0}bar D^0$ using a sample of 657 million $Bbar B$ pairs recorded at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. Both $D^{*0}to
D^0gamma$ and $D^{*0}to D^0pi^0$ decay modes are used. We find a peak of $50.1^{+14.8}_{-11.1}$ events with a mass of $(3872.9^{+0.6 +0.4}_{-0.4 -0.5}){rm MeV}/c^2$, a width of $(3.9^{+2.8 +0.2}_{-1.4 -1.1}){rm MeV}/c^2$ and a product branching fraction ${cal B}(Bto X(3872)K)times{cal B}(X(3872)to D^{*0}bar D^0)=(0.80pm0.20pm0.10)times10^{-4}$, where the first errors are statistical and the second ones are systematic. The significance of the signal is $6.4sigma$. The difference between the fitted mass and the $D^{*0}bar D^0$ threshold is calculated to be $(1.1^{+0.6 +0.1}_{-0.4 -0.3}){rm MeV}/c^2$. We also obtain an upper limit on the product of branching fractions ${cal B}(Bto Y(3940)K)times{cal B}(Y(3940)to D^{*0}bar D^0)$ of $0.67times10^{-4}$ at 90% CL.
