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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