In a search for B→cc̅ γK decays with the BABAR detector, where cc̅ includes J/ψ and ψ(2S), and K includes K±, KS0, and K*(892), we find evidence for X(3872)→J/ψγ and X(3872)→ψ(2S)γ with 3.6σ and 3.5σ significance, respectively. We measure the product of branching fractions B(B±→X(3872)K±)×B(X(3872)→J/ψγ)=[2.8±0.8(stat)±0.1(syst)]×10-6 and B(B±→X(3872)K±)×B(X(3872)→ψ(2S)γ)=[9.5±2.7(stat)±0.6(syst)]×10-6.
