Question

find the value of ( x ). note that ( ab = x ), ( bc = 4 ), and ( cd = 5 ).

Explanation:

Step1: Recall secant-secant power theorem

If a secant segment $BA$ and an extended secant segment $BD$ are drawn from external point $B$ to a circle, then $AB^2 = BC \times BD$.

Step2: Calculate length of BD

$BD = BC + CD = 4 + 5 = 9$

Step3: Substitute values into theorem

$x^2 = 4 \times 9$

Step4: Solve for x

$x^2 = 36$
$x = \sqrt{36} = 6$ (length is positive)

Answer:

$6$