Answer
AB=16
Work Step by Step
Angles ODA and BDP are congruent because they are vertical angles. Angles B and A are both right angles because they connect a radius to a tangent at the point of tangency, so they are also congruent. Therefore triangles ADO and BDP are similar proven by AA.
$\frac{OA}{PB}$=$\frac{OD}{20-OD}$
$\frac{3}{9}$=$\frac{OD}{20-OD}$
60-3OD=9OD
12OD=60
OD=5
DP=20-OD
DP=15
AD$^2$=5$^2$-3$^2$
AD$^2$=16
AD=4
DB$^2$=15$^2$-9$^2$
DB$^2$=144
DB=12
AB=AD+DB
AB=4+12
AB=16
