Question

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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

By the secant-tangent theorem: (tangent)^2 = (external secant)(whole secant). Here 12^2 = 10(10 + a), so 10(a + 10) = 12^2.

(That corresponds to the choice written as 10(a + 10) = 122.)