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Q6.

Expert-verifiedFound in: Page 335

Book edition
Student Edition

Author(s)
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages
227 pages

ISBN
9780395977279

**$\overline{RS}$ and $\overline{TU}$ are common internal tangents to the circles. If $RZ=4\xb77$ and $ZU=7\xb73$, Find $RS$ and $TU$.**

Value of,** $RS=12$**

And, $TU=12$.

The figure:

$RZ=4.7$ And $ZU=7.3$

Theorem $9\xb71$ Corollary:

Tangents to a circle from a point are congruent.

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 $9\xb71$ 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 $9\xb71$ corollary, it can be said that:

$SZ=UZ=7.3$ ….. (2)

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

And

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

Therefore, Value of,** $RS=12$**, and $TU=12$.

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