Answer
$AB = 15$
Work Step by Step
According to the perpendicular bisector theorem, points lying on the perpendicular bisector of a segment are equidistant from the segment's endpoints.
In the diagram, we see that $\overline{AC}$ is the perpendicular bisector of $\overline{BD}$; therefore, $AD$ is equal to $AB$. So if $AD = 15$, then $AB = 15$.
