Question

Can someone help me find X and the measure of TS? Pleaseee

Answer 1

Given:

QR=20, TS=4x-3, RS=16.

To find:

The value of x and TS.

Solution:

In the figure QR is tangent and RT is secant to the given circle.

According to the secant-tangent theorem, the square of the length of the tangent segment is equal to the product of the lengths of the secant and its external segment, if the tangent and secant are drawn to a  from the an external point.

Using secant-tangent theorem, we get

$QR^2=RS\times RT$

$QR^2=RS\times (TS+RS)$

$20^2=16\times (4x-3+16)$

$400=16\times (4x+13)$

Divide both sides by 16.

$25=4x+13$

Subtracting both sides by 13.

$25-13=4x$

$12=4x$

Divide both sides by 4.

$3=x$

Now,

$TS=4x-3$

$TS=4(3)-3$

$TS=12-3$

$TS=9$

Therefore, the value of x is 3 and the measure of TS is 9 units.