  We study radiative charm decays $D \to P_1 P_2 \gamma$, $P_{1,2}=\pi,K$ in
QCD factorization at leading order and within heavy hadron chiral perturbation
theory. Branching ratios including resonance contributions are around $\sim
10^{-3}$ for the Cabibbo-favored modes into $K \pi \gamma$ and $\sim 10^{-5}$
for the singly Cabibbo-suppressed modes into $\pi^+ \pi^- \gamma, K^+ K^-
\gamma$, and thus in reach of the flavor factories BES III and Belle II. Dalitz
plots and forward-backward asymmetries reveal significant differences between
the two QCD frameworks; such observables are therefore ideally suited for a
data-driven identification of relevant decay mechanisms in the standard-model
dominated $D \to K \pi \gamma$ decays. This increases the potential to probe
new physics with the $D \to \pi^+ \pi^- \gamma$ and $D \to K^+ K^- \gamma$
decays, which are sensitive to enhanced dipole operators. CP asymmetries are
useful to test the SM and look for new physics in neutral $|\Delta C|=1$
transitions. Cuts in the Dalitz plot enhance the sensitivity to new physics due
to the presence of both $s$- and $t,u$-channel intermediate resonances.
