In the figure shown, $AC=13$ and $DC=2$ units. What is the length of the segment $BD$? Express your answer in simplest radical form.
We have this relationship
Angle DAB = Angle CBD
Angle ADB = Angle CDB
So...by AA congruency......Triangle ADB is similar to Triangle BDC
And AD = AC - DC = 13 - 2 = 11
So
AD / DB = BD / DC
AD * DC = BD^2
11 * 2 = BD^2
BD^2 = 22
BD = sqrt (22)
