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Q6.

Expert-verified

Geometry

Found in: Page 335

Book edition Student Edition

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

Pages 227 pages

ISBN 9780395977279

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Short Answer

$\bar{R S}$ and $\bar{T U}$ are common internal tangents to the circles. If $R Z = 4 \cdot 7$ and $Z U = 7 \cdot 3$ , Find $R S$ and $T U$ .

Value of, $R S = 12$

And, $T U = 12$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The figure:

$R Z = 4.7$ And $Z U = 7.3$

Step 2. Concept Used.

Theorem $9 \cdot 1$ Corollary:

Tangents to a circle from a point are congruent.

Step 3. Consider the given figure for further solution.

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

$T Z = R Z = 4.7$ ….. (1)

Similarly, $\bar{U Z}$ and $\bar{S Z}$ are tangents to the bigger circle from the common point $Z$ , so by theorem $9 \cdot 1$ corollary, it can be said that:

$S Z = U Z = 7.3$ ….. (2)

Step 4. Thus, from (1) and (2).

$\begin{matrix} R S = R Z + Z S \\ = 4.7 + 7.3 \\ = 12 \end{matrix}$

And

$\begin{matrix} T U = T Z + Z U \\ = 4.7 + 7.3 \\ = 12 \end{matrix}$

Therefore, Value of, $R S = 12$ , and $T U = 12$ .

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