Question

In the circle provided, what is the value of x?

Answer 1

Answer:

x = 4

Explanation:

Intersecting tangent- secant theorem says that if we have

then

$AB^2=BC*BD$

Now in our case,

AB = 8, BC = x, and CD = 12 + x; therefore, the above formula gives

$8^2=x(x+12)$

Expanding the above gives

$64=x^2+12x$

subtracting 64 from both sides gives

$x^2+12x-64=0$

Using the quadratic formula, the two solutions we get are:

$x=\frac{-12\pm\sqrt{12^2-4(1)(-64)}}{2}$

which we evaluate to get:

$x=\frac{-12\pm20}{2}$

which gives us two solutions:

$\begin{gathered} x=-16 \\ x=4 \end{gathered}$

Since a length cannot be a negative number, x = 4 is our relevant solution.