Question

Which equation results from applying the secant and tangent segment theorem to the figure?

Answer 1

Solution:

The Secant and tangent theorem states that the point where secant and tangent meets ,then square of length of tangent is equal to product of length of two segments .

In the picture depicted below, DE is the Tangent and DB is the length of Secant.Whereas DA is the length of segment which is equal to point of intersection of tangent and secant and secant and circle.

DE²= DA × DB

→12²=10 × (a+10)

Option (C) is correct description.  

Answer 2

1. You must apply the Secant and Tangent segment theorem, which establishes:

 Tangent²=(The whole secant segment)(External secant segment)

 2. The whole secant segment is: AD=a+12

 3. The external secant segment is: BD=10

 4. The tangent segment is: DE=12

 5. Then, you have:

 DE²=ADxBD
 12²=(a+10)10
 10(a+10)=12²

 6. Therefore, the answer is the third option: 10(a+10)=12²