Question

which equation results from applying the tangent segment theorem to the figure? 12(a + 12) = 10² 10 + 12 = a² 10(a + 10) = 12² 10(12) = a²

Explanation:

Step1: Recall the tangent - secant theorem

If a tangent segment and a secant segment are drawn to a circle from an external point, then the square of the length of the tangent segment is equal to the product of the lengths of the entire secant segment and its external part.
Let the tangent length be \(t = 10\), the external part of the secant be \(a\) and the entire secant length be \(a + 12\).
According to the tangent - secant theorem \(t^{2}=a(a + 12)\) (where \(t\) is the tangent length, \(a\) is the external part of the secant and \(a + 12\) is the entire secant).
Substituting \(t = 10\) into the formula, we get \(10^{2}=12(a + 12)\)

Answer:

\(12(a + 12)=10^{2}\)