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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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Title: Understanding Acute Angles in Circles --- **Question:** Is ∠DOC an acute angle? Es ∠DOC un ángulo agudo? --- **Diagram:** This diagram features a circle with center \( O \). There are four labeled points on the circle: \( A \), \( B \), \( C \), and \( D \). Lines \( \overline{OA} \), \( \overline{OB} \), \( \overline{OC} \), and \( \overline{OD} \) are radii of the circle, dividing the circle into four segments. **Explanation:** - **Point \( O \):** The center of the circle. - **Points \( A \), \( B \), \( C \), \( and D \):** Points on the circumference of the circle. - **Radii \( \overline{OA} \), \( \overline{OB} \), \( \overline{OC} \), and \( \overline{OD} \):** These lines are connecting the center \( O \) to the points on the circumference. **Question Details:** - The specific angle in question is ∠DOC, formed by the radii \( \overline{OD} \) and \( \overline{OC} \). - The term "acute angle" refers to an angle that is less than 90 degrees. **Considerations:** To decide whether ∠DOC is acute, observe the position of lines \( \overline{OD} \) and \( \overline{OC} \). If the angle formed between them is less than 90 degrees, it is considered acute. **Answer Box:** To the right of the question is a blank box where the answer can be input. **Button:** Below the diagram and question is an “OK” button to submit the answer. --- **Educational Notes:** - An acute angle is always less than 90 degrees. - A helpful way to visualize this is by comparing the angle to a right angle (which is exactly 90 degrees). ---
Transcribed Image Text:Title: Understanding Acute Angles in Circles --- **Question:** Is ∠DOC an acute angle? Es ∠DOC un ángulo agudo? --- **Diagram:** This diagram features a circle with center \( O \). There are four labeled points on the circle: \( A \), \( B \), \( C \), and \( D \). Lines \( \overline{OA} \), \( \overline{OB} \), \( \overline{OC} \), and \( \overline{OD} \) are radii of the circle, dividing the circle into four segments. **Explanation:** - **Point \( O \):** The center of the circle. - **Points \( A \), \( B \), \( C \), \( and D \):** Points on the circumference of the circle. - **Radii \( \overline{OA} \), \( \overline{OB} \), \( \overline{OC} \), and \( \overline{OD} \):** These lines are connecting the center \( O \) to the points on the circumference. **Question Details:** - The specific angle in question is ∠DOC, formed by the radii \( \overline{OD} \) and \( \overline{OC} \). - The term "acute angle" refers to an angle that is less than 90 degrees. **Considerations:** To decide whether ∠DOC is acute, observe the position of lines \( \overline{OD} \) and \( \overline{OC} \). If the angle formed between them is less than 90 degrees, it is considered acute. **Answer Box:** To the right of the question is a blank box where the answer can be input. **Button:** Below the diagram and question is an “OK” button to submit the answer. --- **Educational Notes:** - An acute angle is always less than 90 degrees. - A helpful way to visualize this is by comparing the angle to a right angle (which is exactly 90 degrees). ---
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