Question

A circle is shown. A secant and tangent intersect at a point outside of the circle. The length of the tangent is x + 2, the length of the external part of the secant is x, and the length of the internal part of the secant is x + 4.
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

Answer 1

Use the power of a point: (external secant)·(whole secant) = (tangent)^2.

External secant = x, whole secant = x + (x + 4) = 2x + 4, tangent = x + 2.

So x(2x + 4) = (x + 2)^2 (option 4).