Question

the rest of the question say what is the length of the tangent line labeled X

Answer 1

To solve this problem, consider the following picture

By the tangent secant segment theorem we have the following equation

$a^2=b\cdot(b+c)$

Note that in our case, we have a=x, b=3 and c=9. So if we replace this values in the equation, we have

$x^2=3\cdot(3+9)=3\cdot12=36$

so, applying the square root on both sides, we get

$x=\sqrt[]{36}=\pm6$

Since x is a distance, it should be strictly positive, so we have that

$x=6$