Question

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

Explanation:

Step1: Recall secant - tangent segment theorem

If a secant segment and a tangent segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external - secant segment.

Step2: Identify segments in the figure

Let the tangent segment be \(DE = 12\), the secant segment be \(DA=10 + a\), and the external - secant segment be \(DB = 10\).
According to the secant - tangent segment theorem, \(DE^{2}=DB\times DA\).
Substituting the values, we get \(12^{2}=10\times(10 + a)\).

Answer:

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