We compute 10 radiative three-body decays of charged charmed mesons $D^+ to P^+ P^0 gamma$ and $D_s to P^+ P^0 gamma$, $P=pi, K$, in leading order QCDF, HH$chi$PT and the soft photon approximation. We work out decay distributions and asymmetries in the standard model and with new physics in the electromagnetic dipole operators. The forward-backward asymmetry is suitable to probe the QCD frameworks, in particular the $s$-channel dependent weak annihilation contributions in QCDF against the markedly different resonance structure in HH$chi$PT. These studies can be performed with Cabibbo-favored modes $D_s to pi^+ pi^0 gamma$, $D^+ to pi^+ overline{K}^0 gamma$ and $D_s to K^+ overline{K}^0 gamma$ with ${cal{O}}(10^{-4}-10^{-3})$-level branching ratio, which are standard model-like and induced by different hadronic dynamics. Understanding of the latter can therefore be improved in a data-driven way and sharpens the interpretation of standard model tests. Singly Cabibbo-suppressed modes such as $ D^+ to pi^+ pi^0 gamma$, $D_s to pi^+ K^0 gamma$, $D_s to K^+ pi^0 gamma$ with branching ratios within $sim 10^{-5}-10^{-4}$ are sensitive to new physics that can be signalled in the forward-backward asymmetry and in the CP-asymmetry of the rate, ideally in the Dalitz region but also in single differential distributions. Results complement those with neutral $D^0 to PP gamma$ decays.
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