Question

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

Explanation:

Step1: Recall the secant-tangent theorem

If a tangent segment of length $t$ and a secant segment with external part $e$ and entire length $e+i$ (where $i$ is the internal part of the secant) are drawn from a point outside a circle, then $t^2 = e \times (e+i)$.

Step2: Identify segment lengths

Tangent length: $x+2$; External secant part: $x$; Entire secant length: $x + (x+4) = 2x+4$.

Step3: Apply the theorem

Substitute into the theorem formula: $(x+2)^2 = x(2x+4)$.

Answer:

D. $x(2x + 4) = (x + 2)^2$