  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 perfectly
satisfied in the rescattering diagrams. A resonance-like structure around the
$B\bar{K}$ threshold, which we denote as $X(5777)$, is predicted to be present
in 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 dynamically
generated hadronic molecule, the $X(5777)$ can be identified as a pure
kinematical effect due to the triangle singularity. Its observation may help to
establish a non-resonance interpretation for some $XYZ$ particles.
