Since those blue lines are perpenticular bisectors, that means they bisect at the midpoint of the line they bisect. That means the the line they bisect gets divided into equal parts. So,
BG must equal AG = 9, because DG bisects AB at the midpoint of D.
AD must equal DB = 6, because DG bisects AB at the midpoint of D.
So, AB =6+6 =12
BG=9
AB=12
