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Segment AD : segment CD = segment BD : segment AD, since triangle ADB is similar to triangle CDA.
Segment BD : segment BA = segment BA : segment CA, since triangle ADB is similar to triangle CDA.
Segment BC : segment BA = segment BA : segment BD, since triangle BCA is similar to triangle BAD.
Segment BA : segment DA = segment AC : segment BA, since triangle BCA is similar to triangle BAD.

hint - wo similar triangles are BCA and BAD

is it D?

hmm ill check

yes - remember the corresponding sides are opposite the equal angles

thank you thank you!!

yw