  The first full angular analysis and an updated measurement of the decay-rate
$CP$ asymmetry of the $D^0 \to \pi^+\pi^-\mu^+\mu^-$ and $D^0 \to
K^+K^-\mu^+\mu^-$ decays are reported. The analysis uses proton-proton
collision data collected with the LHCb detector at centre-of-mass energies of
7, 8 and 13 TeV. The data set corresponds to an integrated luminosity of 9
fb$^{-1}$. The full set of $CP$-averaged angular observables and their $CP$
asymmetries are measured as a function of the dimuon invariant mass. The
results are consistent with expectations from the standard model and with $CP$
symmetry.
