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Q16.

Expert-verified

Geometry

Found in: Page 337

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

$\bar{S R}$ is tangent to $⊙ P$ and $⊙ Q$ .
$Q T = 6, T R = 8, P R = 30 .$
$P Q = ?, P S = ?, S T = ?$

The required values are,

$P Q = 20, P S = 18 and S T = 16$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

$⊙ P$ Any $\bar{S R}$ is tangent to $⊙ P$ and $⊙ Q$ . Also $Q T = 6, T R = 8 and P R = 30$ .

Step 2. Concept used.

Applying Pythagoras in triangle $Δ R T Q$ to find the value of $P Q$ .

Here, $Δ R T Q$ is right angle triangle,

$\begin{array}{l} Q R^{2} = 6^{2} + 8^{2} \\ Q R^{2} = 36 + 64 \\ Q R = 10 \end{array}$

As value of ,

$\begin{array}{l} P Q = 30 - 10 \\ P Q = 20 \end{array}$

Step 3. Let ST be x and SP be y.

Here, $\bar{T Q} | | \bar{S P}$

Then,

$\begin{array}{l} \frac{8}{10} = \frac{x}{20} \\ x = \frac{8 \cdot 20}{10} \\ x = 16 \end{array}$

Same way,

$\begin{array}{l} \frac{8}{6} = \frac{24}{y} \\ y = \frac{24 \cdot 6}{8} \\ y = 18 \end{array}$

Therefore, the values are, $P Q = 20, P S = 18 and S T = 16$ .

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