Chapter 9: Q16. (page 337)

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

Short Answer

Expert verified

The required values are,

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

Step by step solution

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

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

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SR¯ is tangent to ⊙P and ⊙Q.QT=6,TR=8,PR=30.PQ=?,PS=?,ST=?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Discrete Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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