It is tempting to suppose that BD=DC, ie that D is the midpoint of BC.
We start by exploring this conjecture (or rather its converse*), namely that
"If D is the midpoint of BC, then DA bisects the angle at A".

*We have chosen the converse because it is often easier to judge whether a line has been bisected than whether an angle has been bisected.

a high-res pdf file of this new GEOaa-zz task