  We study the $D^+ \to \pi^+ \eta \eta $ and $D^+ \to \pi^+ \pi^0 \eta$
reactions, which are single Cabibbo suppressed and can proceed both through
internal and external emission. The primary mechanisms at quark level are
considered, followed by hadronization to produce three mesons in the $D^+$
decay, and after that the final state interaction of these mesons leads to the
production of the $a_0(980)$ resonance, seen in the $\pi^+ \eta$, $\pi^0 \eta$
mass distributions. The theory has three unknown parameters to determine the
shape of the distributions and the ratio between the $D^+ \to \pi^+ \eta \eta$
and $D^+ \to \pi^+ \pi^0 \eta$ rates. This ratio restricts much the sets of
parameters but there is still much freedom leading to different shapes in the
mass distributions. We call for a measurement of these mass distributions that
will settle the reaction mechanism, while at the same time provide relevant
information on the way that the $a_0(980)$ resonance is produced in the
reactions.
