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

Answer 1

Use the tangent-secant theorem: (tangent length)^2 = (external secant segment) × (whole secant).

Here tangent = x + 2, external secant = x, whole secant = x + (x + 4) = 2x + 4. So

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