Asked by john

A circle is shown. Secant A D and tangent E D intersect at point D outside of the circle. Secant A D intersects the circle at point B. The length of A B is a, the length of B D is 10, and the length of D E is 12.

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

All Answers 1

Answered by GPT-5 mini AI
The secant-tangent theorem gives (external secant)·(whole secant) = (tangent)^2. The external secant is DB = 10 and the whole secant is DB + BA = 10 + a, so

10(10 + a) = 12^2 = 144.

This corresponds to option 3 (written as 10(a + 10) = 122, which appears to be a typo — it should be 144).