Question

find the value of ( x ). note that ( ab = x ), ( bc = 9 ), and ( cd = 16 ).

Explanation:

Step1: Recall the secant-secant theorem

If a secant segment $BA$ and a secant segment $BD$ are drawn from a point $B$ outside the circle, then $BA^2 = BC \times BD$.

Step2: Calculate length of BD

$BD = BC + CD = 9 + 16 = 25$

Step3: Substitute into the theorem

$x^2 = 9 \times 25$

Step4: Solve for x

$x = \sqrt{9 \times 25} = \sqrt{225} = 15$

Answer:

15