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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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### Circle Geometry: Understanding the Inscribed Angle #### Diagram Explanation: The image illustrates a geometric construction within a circle. Below is a detailed description of each element: 1. **Circle**: A circle is defined with a pink circumference. 2. **Center Point**: The circle's center, marked by a green dot. 3. **Triangles**: Two green lines from the circle’s center intersect the circumference, forming two triangles. A green triangle is also visible with one vertex at the circle's center and one along the circumference. 4. **Angle**: An inscribed angle, marked as 73°, is formed at one vertex of the triangle. 5. **Arc**: A purple arrow indicates the arc between two points on the circle’s circumference that correspond to the sides meeting at the 73° angle. 6. **Blank Rectangle**: A white rectangular label connected to the purple arrow, left empty, possibly intended for additional information or labeling. #### Key Concept: - The angle of 73° is the inscribed angle subtended by an arc on the circumference of the circle. - The inscribed angle, which is in degrees, is always half the measure of the central angle subtending the same arc. #### Applications: Understanding inscribed angles is crucial in geometry, especially for solving problems involving circles. This concept is widely applied in various fields, including engineering, architecture, and astronomy. #### Practice Problem: Calculate the central angle if the inscribed angle is 73°. **Solution:** Given: Inscribed Angle = 73° Using the formula: Central Angle = 2 * Inscribed Angle Therefore, Central Angle = 2 * 73° = 146° This fundamental property of circles provides a basis for more complex geometric problem-solving.
Transcribed Image Text:### Circle Geometry: Understanding the Inscribed Angle #### Diagram Explanation: The image illustrates a geometric construction within a circle. Below is a detailed description of each element: 1. **Circle**: A circle is defined with a pink circumference. 2. **Center Point**: The circle's center, marked by a green dot. 3. **Triangles**: Two green lines from the circle’s center intersect the circumference, forming two triangles. A green triangle is also visible with one vertex at the circle's center and one along the circumference. 4. **Angle**: An inscribed angle, marked as 73°, is formed at one vertex of the triangle. 5. **Arc**: A purple arrow indicates the arc between two points on the circle’s circumference that correspond to the sides meeting at the 73° angle. 6. **Blank Rectangle**: A white rectangular label connected to the purple arrow, left empty, possibly intended for additional information or labeling. #### Key Concept: - The angle of 73° is the inscribed angle subtended by an arc on the circumference of the circle. - The inscribed angle, which is in degrees, is always half the measure of the central angle subtending the same arc. #### Applications: Understanding inscribed angles is crucial in geometry, especially for solving problems involving circles. This concept is widely applied in various fields, including engineering, architecture, and astronomy. #### Practice Problem: Calculate the central angle if the inscribed angle is 73°. **Solution:** Given: Inscribed Angle = 73° Using the formula: Central Angle = 2 * Inscribed Angle Therefore, Central Angle = 2 * 73° = 146° This fundamental property of circles provides a basis for more complex geometric problem-solving.
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