The rates of the X(3872)→π0π0χc1 and X(3872)→π+π−χc1 decays are estimated in the model of the triangle loop diagrams with charmed D*D¯D and D¯*DD¯ mesons in the loops. There are the triangle logarithmic singularities in the physical region of the X(3872)→π0π0χc1 decay which manifest themselves as narrow peaks in the π0χc1 mass spectrum near the D0D¯0 threshold. The model predicts approximately the same branching fractions of the X(3872)→π0π0χc1 and X(3872)→π+π−χc1 decays at the level of about (0.8–1.7)×10−4. A distinct prediction of the model is the value of the ratio R=B(X(3872)→π+π−χc1)/B(X(3872)→π0π0χc1)≈1.1. It weakly depends on the X(3872) resonance parameters and indicates a significant violation of the isotopic symmetry according to which one would expect R=2. Published by the American Physical Society 2024