Given:
The objective is to find the value of x.
Step-by-step explanation:
The general formula using tangent segment theorem,
![x^2=6*(6+18)\text{ . . . .(1)}](https://img.qammunity.org/2023/formulas/mathematics/college/nkyfa9nto0qh8vm3lyz7g68do193trowl7.png)
On further solving the equation (1).
![\begin{gathered} x^2=6*(24) \\ x^2=144 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/jicu0giesxsy2kvgwc7v96nfc9707z05gq.png)
Now, taking square root on both sides,
![\begin{gathered} \sqrt[]{x^2}=\sqrt[]{144} \\ x=12 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/26n2xx46335sp1xof93w1rdl3df0pk2nih.png)
Thus, the value of x is 12.
Hence, option (3) is the correct answer.