Question

Find the length of UT¯¯¯¯¯¯¯+CV¯¯¯¯¯¯¯¯. A. 4x + 35B. 53C. 59D. 65

Answer 1

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:

`\begin{gathered} UT=UW+WT=(2x+2)+14=2x+16 \\ CV=CW+WV=12+(2x+5)=2x+17 \end{gathered}`

And there is a relation between the chords that are as follows:

`12(2x+5)=14(2x+2)`

We will solve the last equation to find the value of x:

`\begin{gathered} 24x+60=28x+28 \\ 24x-28x=28-60 \\ -4x=-32 \\ \\ x=(-32)/(-4)=8 \end{gathered}`

Substitute x = 8 into the expressions of UT and CV:

`\begin{gathered} UT=2*8+16=32 \\ CV=2*8+17=33 \end{gathered}`

So, the value of UT + CV = 32 + 33 = 65

So, the answer will be D. 65