Question

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

Answer 1

The equation which is results from applying the secant and tangent segment theorem to the provided figure is,

$x(2x +4) = (x +2)^2$

What is secant and tangent segment theorem?

The secant-tangent theorem tells the relation of the line segment made by a tangent and the secant lines with the connected circle.

According to this theorem, if the tangent and secant segments are drawn from an exterior point, then the square of this tangent segment is equal to the product of the secant segment and the line segment from that exterior point.

The image of the given problem is attached below. In the attached image, the tangent is given as,

$T=x+2$

The secant is shown in the image has the value,

$S=x+x+4\\S=2x+4$

Now according to the secant tangent theorem,

$x(2x +4) = (x +2)^2$

Hence, the equation which is results from applying the secant and tangent segment theorem to the provided figure is,

$x(2x +4) = (x +2)^2$

Learn more about the secant-tangent segment theorem here;

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