Answer:
Step-by-step explanation:
We know that SU and VT are chords. If the intersect at point R, we can define the following proportion
[tex]\frac{RS}{RT} =\frac{RV}{RU}[/tex]
Where
[tex]RS=SR=x+6\\RT=x+4\\VR=RV=x+1\\RU=x[/tex]
Replacing all these expressions, we have
[tex]\frac{x+6}{x+4} =\frac{x+1}{x}[/tex]
Solving for [tex]x[/tex], we have
[tex]x(x+6)=(x+4)(x+1)\\x^{2} +6x=x^{2} +x+4x+4\\6x-5x=4\\x=4[/tex]
Now, notice that chord VT is form by the sum of RT and RV, so
[tex]VT=VR+RT\\VT=x+1+x+4\\VT=2x+5[/tex]
Replacing the value of the variable
[tex]VT=2(4)+5\\VT=8+5\\VT=13[/tex]
Therefore, the length of the line segment VT is 13 units.
