Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
### Diagram Description
The provided diagram illustrates a circle centered at point \( J \). Inside the circle, there are two radii, \( \overline{JK} \) and \( \overline{JL} \), forming an angle \( \angle KJL \).
### Options
Select the correct length of \( \overline{JK} \):
- \( \boxed{JK = 5} \)
- \( \boxed{JK = 10} \)
- \( \boxed{JK = 6} \)
- \( \boxed{JK = 3} \)
### Steps to Solve
1. Calculate the circumference of the circle using the formula for arc length.
2. Use the given arc length to find the radius of the circle.
3. Compare the possible answers with the calculated radius.
### Explanation of the Diagram
The diagram shows a circle with points \( J \), \( K \), and \( L \).
- \( J \) is the center of the circle.
- \( \overline{JK} \) and \( \overline{JL} \) are radii of the circle.
- The angle \( \angle KJL \) is given to be \( 72^\circ \).
- The arc \( \overset{\frown}{KL} \) has a length of \( \frac{6}{5} \pi \).
- The task is to find the length of \( \overline{JK} \), which is the radius of the circle.
### Solution
```markdown
Given:
- \( m \angle KJL = 72^\circ \)
- \( \overset{\frown}{KL} = \frac{6}{5} \pi \)
Arc Length Formula:
\[ \text{Arc Length} = 2 \pi r \times \left( \frac{\theta}{360} \right) \]
Where:
- \( \theta = 72^\circ \)
- Arc Length \( = \frac{6}{5} \pi \)
\[ \frac{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb6a3e0a-0e9e-4eb9-b3f8-cac67ff0b1b6%2Fad0c0a41-a107-4235-8db5-633367d9bd5d%2Fnwxh1h9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
In circle \( J \), \( m \angle KJL = 72^\circ \) and the length of \( \overset{\frown}{KL} = \frac{6}{5} \pi \). Find the length of \( \overline{JK} \).
### Diagram Description
The provided diagram illustrates a circle centered at point \( J \). Inside the circle, there are two radii, \( \overline{JK} \) and \( \overline{JL} \), forming an angle \( \angle KJL \).
### Options
Select the correct length of \( \overline{JK} \):
- \( \boxed{JK = 5} \)
- \( \boxed{JK = 10} \)
- \( \boxed{JK = 6} \)
- \( \boxed{JK = 3} \)
### Steps to Solve
1. Calculate the circumference of the circle using the formula for arc length.
2. Use the given arc length to find the radius of the circle.
3. Compare the possible answers with the calculated radius.
### Explanation of the Diagram
The diagram shows a circle with points \( J \), \( K \), and \( L \).
- \( J \) is the center of the circle.
- \( \overline{JK} \) and \( \overline{JL} \) are radii of the circle.
- The angle \( \angle KJL \) is given to be \( 72^\circ \).
- The arc \( \overset{\frown}{KL} \) has a length of \( \frac{6}{5} \pi \).
- The task is to find the length of \( \overline{JK} \), which is the radius of the circle.
### Solution
```markdown
Given:
- \( m \angle KJL = 72^\circ \)
- \( \overset{\frown}{KL} = \frac{6}{5} \pi \)
Arc Length Formula:
\[ \text{Arc Length} = 2 \pi r \times \left( \frac{\theta}{360} \right) \]
Where:
- \( \theta = 72^\circ \)
- Arc Length \( = \frac{6}{5} \pi \)
\[ \frac{
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