LAUSR

We calculate the cross section for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into ${D}^{*0}{\overline{D}}^{0}+\ensuremath{\gamma}$ at center-of-mass energies near the ${D}^{*0}{\overline{D}}^{*0}$ threshold under the assumption that $X(3872)$ is a weakly bound charm-meson molecule. The Dalitz plot has a ${\overline{D}}^{*0}$ resonance band in the squared invariant mass $t$ of ${\overline{D}}^{0}\ensuremath{\gamma}$. In the limit as the decay width of the ${D}^{*0}$ goes to 0, the Dalitz plot also has a narrow band in the squared invariant mass $u$ of ${D}^{*0}{\overline{D}}^{0}$ from a charm-meson triangle singularity. At the physical value of the ${D}^{*0}$ width, the narrow band reduces to a shoulder. Thus, the triangle singularity cannot be observed directly as a peak in a differential cross section as a function of $u$. It may however be observed indirectly as a local minimum in the $t$ distribution for events with $u$ below the triangle singularity. The minimum is produced by the Schmid cancellation between triangle loop diagrams and a tree diagram. The observation of this minimum would support the identification of $X(3872)$ as a weakly bound charm-meson molecule.