Question

Find the value of X

Answer 1

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.

$AB^2=BC\times BD$

$12^2=9\times (9+x)$

$144=81+9x$

Subtract 81 from both sides.

$144-81=81+9x-81$

$63=9x$

Divide by 9 on both sides.

$\frac{63}{9} =\frac{9x}{9}$

$9=x$

The value of x is 9.