Given the figure of a circle
As shown, there are two chords UT and CV that intersection at point W
The length of the chords are as follows:
[tex]\begin{gathered} UT=UW+WT=(2x+2)+14=2x+16 \\ CV=CW+WV=12+(2x+5)=2x+17 \end{gathered}[/tex]
And there is a relation between the chords that are as follows:
[tex]12(2x+5)=14(2x+2)[/tex]
We will solve the last equation to find the value of x:
[tex]\begin{gathered} 24x+60=28x+28 \\ 24x-28x=28-60 \\ -4x=-32 \\ \\ x=\frac{-32}{-4}=8 \end{gathered}[/tex]
Substitute x = 8 into the expressions of UT and CV:
[tex]\begin{gathered} UT=2*8+16=32 \\ CV=2*8+17=33 \end{gathered}[/tex]
So, the value of UT + CV = 32 + 33 = 65
So, the answer will be D. 65
