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
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![**Title: Understanding Circles and Their Components**
**Definition:**
A circle is a simple closed shape consisting of all points in a plane that are at a given distance from a given point, the center.
**Components to Identify:**
1. **Center of the Circle:**
- The center of the circle is labeled as point \( Q \). It is the point from which all points on the circle are equidistant.
2. **Central Angle:**
- The central angle is an angle whose vertex is the center of the circle, and its sides are radii. In the diagram, angle \( LQN \) is a central angle.
3. **Semicircle:**
- A semicircle is half of a circle, formed by dividing a circle along its diameter. In the diagram, the arc \( PMN \) represents a semicircle.
**Diagram Explanation:**
The diagram shows a circle with:
- Points \( P, L, M, N, O \) on the circumference.
- Line segments radiating from the center \( Q \) to points \( L \), \( O \), and \( N \).
- Arc \( PMN \) forming a semicircle.
- Central angle \( \angle LQN \).
**Conclusion:**
Understanding these basic components of a circle is essential for exploring more complex geometrical concepts and problems involving circles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d7ffa32-c081-4b73-abc9-a0664169f2ac%2Fca2a2efc-7bc4-454c-a2dd-90403dccd329%2Fxpchxjr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Circles and Their Components**
**Definition:**
A circle is a simple closed shape consisting of all points in a plane that are at a given distance from a given point, the center.
**Components to Identify:**
1. **Center of the Circle:**
- The center of the circle is labeled as point \( Q \). It is the point from which all points on the circle are equidistant.
2. **Central Angle:**
- The central angle is an angle whose vertex is the center of the circle, and its sides are radii. In the diagram, angle \( LQN \) is a central angle.
3. **Semicircle:**
- A semicircle is half of a circle, formed by dividing a circle along its diameter. In the diagram, the arc \( PMN \) represents a semicircle.
**Diagram Explanation:**
The diagram shows a circle with:
- Points \( P, L, M, N, O \) on the circumference.
- Line segments radiating from the center \( Q \) to points \( L \), \( O \), and \( N \).
- Arc \( PMN \) forming a semicircle.
- Central angle \( \angle LQN \).
**Conclusion:**
Understanding these basic components of a circle is essential for exploring more complex geometrical concepts and problems involving circles.
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