Chapter 9: Q17. (page 337)

$\bar{J K}$ is tangent to $⊙ P$ and $⊙ Q$ .
$J K = ?$

Short Answer

Expert verified

The given quadrilateral $J P Q K$ must be a Trapezium.

Step by step solution

Step 1. Given information.

The figure here given is,

$J K$ is tangent to the circle with centers $P$ and $Q$ .

Step 2. Draw the construction in figure.

The measures of the sides are,

$\begin{array}{l} P Q = 17 \\ Q K = 3 \\ P D = 3 \\ P J = 11 \end{array}$

$O T$ is required to find the measures of sides $J D$ and $J K$ .

Now,

$P J ⊥ J K$ And $Q K ⊥ J K$

Joint $P J$ and $Q K$ and make a line parallel to $P Q$ that is $D K$ .

Then, it implies that,

$P Q = D K (= 17)$ ........(1)

To find $D K$ ,

Step 3. Concept used.

Triangle $J K D$ is a right angle triangle so one can use Pythagoras Theorem,

The measures of sides in this right angle triangle are,

$\begin{array}{l} D K = 17 \\ J D = 11 - 3 \\ = 8 \end{array}$

Step 4. Use Pythagoras Theorem as follows.

$\begin{array}{l} D K ² = J K ² + J D ² \\ 17 ² = J K ² + 8 ² \\ 289 = J K ² + 64 \\ J K ² = 289 - 64 \\ = 225 \end{array}$

Take positive square to get,

$J K = 15$

So, the required length is $J K = 15$ .

In quadrilateral $P Q J K$ , sum one pair of adjacent angle is $180 °$ .

Therefore, it can be concluded that the opposite sides is parallel.

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$\bar{J K}$ is tangent to $⊙ P$ and $⊙ Q$ .
$J K = ?$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Draw the construction in figure.

Step 3. Concept used.

Step 4. Use Pythagoras Theorem as follows.

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JK¯ is tangent to ⊙P and ⊙Q. JK=?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Draw the construction in figure.

Step 3. Concept used.

Step 4. Use Pythagoras Theorem as follows.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

$\bar{J K}$ is tangent to $⊙ P$ and $⊙ Q$ .
$J K = ?$