Question

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

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

$10(a+10)=(12)^2$

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.

In the figure attached below for the circle O, the length of the DB is,

$DB=10$

Here, the line segment AB is a unit. Thus, the length of line segment AD is,

$AD=a+10$

The length of the tangent DE is 12 units. Thus, by the above theorem,

$(DE)^2=AB\times BD\\(12)^2=(a+10)\times10$

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

$10(a+10)=(12)^2$

Learn more about the secant-tangent segment theorem here;

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