Question

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

Answer 1

The secant-tangent theorem gives (external secant)·(whole secant) = (tangent)^2. Here external secant = 10, whole secant = 10 + a, tangent = 12. So

10(a + 10) = 12^2,

which corresponds to option 3.