Question

Which equation results from applying the secant and
tangent segment theorem to this figure?
O x(x + 2) = (x+4)
O x(x + 4) = (x + 2)
O x(x + 4) = (x + 2)2
O x(2x + 4) = (x + 2)2
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Answer 1

Answer: x(2x+4) = (x+2)^2

Answer 2

The equation that results from applying the tangent segment theorem to the given figure is; x(2x + 4) = (x + 2)²

What is the correct equation?

According to the secant and tangent segment theorem, the square of the tangent line is equal to the product of the secant segments. This is;

Tangent² = whole secant segment × External secant segment

DE² = AD × BD

We are given that;

DE = x

AD = 2x + 4

BD = x + 2

Thus, we have;

x(2x + 4) = (x + 2)²

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