Given:
A figure of a circle. A secant SU and a tangent SR is drawn to the circle from the external point S.
To find:
The measure of the line segment TU.
Solution:
According to the secant tangent segment theorem, the square of tangent is equal to the product of secant and external segment of the secant.
Using secant tangent segment theorem, we get
[tex]SR^2=SU\times ST[/tex]
[tex](40)^2=(32+2x-2)\times (32)[/tex]
[tex]1600=(30+2x)(32)[/tex]
[tex]1600=960+64x[/tex]
Subtract both sides by 960.
[tex]1600-960=64x[/tex]
[tex]640=64x[/tex]
Divide both sides by 64.
[tex]\dfrac{640}{64}=x[/tex]
[tex]10=x[/tex]
Now, the measure of the line segment TU is:
[tex]TU=2x-2[/tex]
[tex]TU=2(10)-2[/tex]
[tex]TU=20-2[/tex]
[tex]TU=18[/tex]
Therefore, the correct option is C.
