Question

which equation results from applying the secant and tangent segment theorem to this figure?
○ x(x + 2)=(x + 4)
○ x(x + 4)=(x + 2)
○ x(x + 4)=(x + 2)^2
○ x(2x + 4)=(x + 2)^2

Explanation:

Step1: Recall secant - tangent segment theorem

If a secant segment and a tangent segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external - secant segment.
The length of the tangent segment is \(x + 2\). The length of the secant segment is \(x+(x + 4)=2x + 4\) and the length of its external - secant segment is \(x\).

Step2: Apply the theorem

According to the secant - tangent segment theorem, \(x(2x + 4)=(x + 2)^2\).

Answer:

\(x(2x + 4)=(x + 2)^2\)