Constraints on the CKM angle $\gamma$ from $B^\pm\rightarrow Dh^\pm$ decays using $D\rightarrow h^\pm h^{\prime\mp}\pi^0$ final states

A data sample collected with the LHCb detector, corresponding to an integrated luminosity of $9~{\rm fb}^{-1}$, is used to measure $CP$ observables in $B^\pm \to D h^\pm$ decays, where $h^{(\prime)}$ is either a kaon or a pion, and the neutral $D$ meson decay is reconstructed in the three-body final states $K^\pm \pi^\mp \pi^0$, $\pi^\pm \pi^\mp \pi^0$, and $K^\pm K^\mp \pi^0$. The most suppressed of these modes, $B^\pm \to [\pi^\pm K^\mp \pi^0]_D K^\pm$, is observed with a significance greater than seven standard deviations and constraints on the CKM angle $\gamma$ are calculated from the combination of the measurements.