Applying the secant-tangent theorem, the length of DE is: 25.
What is the Secant-tangent Theorem?
The secant-tangent theorem states that when a secant and a tangent intersect outside a circle, the square of the tangent segment equals the product of the secant and its external segment.
Given the following:
- AE = 15 (tangent)
- CE = 9 (external segment of secant DE)
Applying the secant-tangent theorem, we would have:
AE² = CE × DE
Let DC = x
DE = x + 9
Plug the values into the equation:
15² = 9 × (x + 9)
225 = 9x + 81
225 - 81 = 9x
144 = 9x
144/9 = x
x = 16
DE = x + 9
Plug in the value of x
DE = 16 + 9
DE = 25.
Therefore, applying the secant-tangent theorem, the length of DE is: 25.
Learn more about the secant-tangent theorem on:
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