The value of x is 9.
Solution:
AB is a tangent and BD is the secant.
AB = 12, BC = 9 and CD = x
BD = BC + CD
BD = 9 + x
The product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
[tex]AB^2=BC\times BD[/tex]
[tex]12^2=9\times (9+x)[/tex]
[tex]144=81+9x[/tex]
Subtract 81 from both sides.
[tex]144-81=81+9x-81[/tex]
[tex]63=9x[/tex]
Divide by 9 on both sides.
[tex]$\frac{63}{9} =\frac{9x}{9}[/tex]
[tex]9=x[/tex]
The value of x is 9.
