Question

Find the length of x. Assume that lines which appear to be tangent to the circle are tangent.

A) 32

B) 35

C)38

D)42

Answer 1

Correct me if I’m wrong but I think it’s B

Answer 2

The length of X=32

Correct answer is A.

The image shows a circle with a tangent and a secant line coming from a common point outside the circle. To find the length of x , we use the tangent-secant theorem, which states that if a tangent and a secant (or another tangent) emanate from a common external point, then the square of the length of the tangent segment is equal to the product of the whole secant segment length and its external part.

Mathematically, this can be expressed as:

`\[ (\text{Tangent segment length})^2 = (\text{External part of secant}) * (\text{Whole length of secant}) \]`

The given lengths in the image are the tangent segment (30 units) and the external part of the secant (18 units). Let's denote the whole length of the secant as a . We can then set up the equation:

`\[ 30^2 = 18 * a \]`

a=50

Now we can solve for x . Let's do that.

The length of a is 50 units.

Thus, the value of X = 50-18 = 32