Question

segment ab is tangent to the circle at point b. which equation describes the relationship between the tangent and secant line segments?
a. (ab)^2 = (ac)(ad)
b. (ad)^2 = (ac)(ab)
c. ab = 1/2(ac + ad)
d. (ab)^2 = (ac)(cd)

Explanation:

Step1: Recall the tangent - secant theorem

If a tangent segment \(AB\) and a secant segment \(AD\) (where \(AC\) is the external part of the secant) are drawn to a circle from an external point \(A\), the formula is \((\text{tangent segment})^2=\text{(external part of secant)}\times(\text{entire secant segment})\).

Step2: Identify the segments

Here, the tangent segment is \(AB\), the external part of the secant is \(AC\), and the entire secant segment is \(AD\).
So, by the tangent - secant theorem, \((AB)^{2}=(AC)(AD)\)

Answer:

A. \((AB)^{2}=(AC)(AD)\)