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Define a circle. Identify each of the following: the center of the circle, a central angle, and semicircle. P. M

Define a circle. Identify each of the following: the center of the circle, a central angle, and semicircle. P. M

Elementary Geometry For College Students, 7e
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.
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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