Chapter 9.2, Problem 6WE

Solution

To find: $RS$ and $TU$

  $RS=12$

  $TU=12$

Given:

The figure:

$RZ=4.7$ And $ZU=7.3$

Concept Used:

Theorem 9-1 Corollary: Tangents to a circle from a point are congruent.

Explanation:

Consider the given figure:

From the above figure it is clear that $\overline{RZ}$ and $\overline{TZ}$ are tangents to the smaller circle from the common point Z, so by theorem 9-1 corollary, it can be said that:

$TZ=RZ=4.7$ ….. (1)

Similarly, $\overline{UZ}$ and $\overline{SZ}$ are tangents to the bigger circle from the common point Z, so by theorem 9-1 corollary, it can be said that:

  $SZ=UZ=7.3$ ….. (2)

Thus, from (1) and (2),

  $\begin{array}{c}RS=RZ+ZS\\ =4.7+7.3\\ =12\end{array}$

And

  $\begin{array}{c}TU=TZ+ZU\\ =4.7+7.3\\ =12\end{array}$