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

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