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We investigate the process $B_c^+\to B_s^0\pi^+\pi^0$ via $B\bar{K}^*$rescattering. The kinematic conditions for triangle singularities are perfectlysatisfied in the rescattering diagrams. A resonance-like structure around the$B\bar{K}$ threshold, which we denote as $X(5777)$, is predicted to be presentin the invariant mass distribution of $B_s^0 \pi^+$. Because the relative weak$B\bar{K}$ $(I=1)$ interaction does not support the existence of a dynamicallygenerated hadronic molecule, the $X(5777)$ can be identified as a purekinematical effect due to the triangle singularity. Its observation may help toestablish a non-resonance interpretation for some $XYZ$ particles.

Generating a resonance-like structure in the reaction $B_c\to B_s \pi\pi$