Question

secants $overline{rt}$ and $overline{tv}$ intersect at point $t$. $overline{st}=4$, $overline{rs}=16$, $overline{tu}=8$, $overline{uv}=x$. what is the value of $x$? a. 2 b. 8 c. 12 d. 32

Explanation:

Step1: Apply secant - secant rule

When two secants $\overline{RT}$ and $\overline{TV}$ intersect outside a circle, the rule is $ST\times RT=UT\times TV$. First, find $RT = RS + ST=16 + 4=20$ and $TV=TU + UV=8 + x$.

Step2: Substitute values into the formula

We have $4\times20=8\times(8 + x)$.

Step3: Solve the equation

First, simplify the left - hand side: $4\times20 = 80$. Then the equation becomes $80=8\times(8 + x)$. Divide both sides by 8: $\frac{80}{8}=8 + x$, so $10 = 8+x$. Subtract 8 from both sides: $x=10 - 8=2$.

Answer:

A. 2