1. The problem asks to find the equation resulting from applying the secant and tangent segment theorem to the given figure. 2. The secant and tangent segment theorem states that if a tangent segment and a secant segment are drawn from a point outside a circle, then: $$\text{(tangent segment)}^2 = \text{(external part of secant)} \times \text{(whole secant)}$$ 3. In the figure, segment DE is tangent to the circle, so its length squared equals the product of the external part and the whole length of the secant segment DB + BE. 4. Given: - Tangent segment length = 10 - External part of secant = 12 - Whole secant length = $a + 12$ 5. Applying the theorem: $$10^2 = 12 \times (a + 12)$$ 6. This matches the equation: $$12(a + 12) = 10^2$$ which is the first option. Final answer: $$12(a + 12) = 10^2$$