Given the circle below with secants $\overline{S T U}$ and $\overline{W V U}$. If $W U=20, W V=7$ and $T U=11$, find the length of $\overline{S T}$. Round to the nearest tenth if necessary.
Solution
Step 1 ：Given the circle with secants $\overline{S T U}$ and $\overline{W V U}$. We know that $W U=20, W V=7$ and $T U=11$. We need to find the length of $\overline{S T}$.
Step 2 ：From the properties of secants, we know that the product of the lengths of the segments of one secant is equal to the product of the lengths of the segments of the other secant. In other words, $(S T \times T U) = (W V \times W U)$.
Step 3 ：We can rearrange this equation to solve for $S T$: $S T = \frac{(W V \times W U)}{T U}$.
Step 4 ：Substitute the given values into this equation to find the length of $S T$.
Step 5 ：$W U = 20$, $W V = 7$, $T U = 11$, $S T = \frac{(7 \times 20)}{11} = 12.727272727272727$
Step 6 ：The question asks for the answer to be rounded to the nearest tenth if necessary. Therefore, we need to round our answer.
Step 7 ：$S T_{rounded} = 12.7$
Step 8 ：Final Answer: The length of $\overline{S T}$ is \(\boxed{12.7}\).
