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Point O is the center of the circle. Determine m BD. A 120° А 120° 90° C 150° D 60°

Point O is the center of the circle. Determine m BD. A 120° А 120° 90° C 150° D 60°

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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### Geometry Problem: Angle Determination in a Circle **Problem Statement:** Point \( O \) is the center of the circle. Determine \( m \angle BD \). **Diagram Explanation:** The given diagram is a circle with center \( O \). The circle has four labeled points on its circumference: \( A \), \( B \), \( C \), and \( D \). The points are positioned such that: - \( \angle AOB \) is a straight line passing through the center \( O \). - \( \overline{OC} \) is a radius that forms a right angle (\(90^\circ\)) with \( \overline{AB} \). - There is an angle \( \angle DOC \) marked as \( 120^\circ \). **Options:** A. \( 120^\circ \) B. \( 90^\circ \) C. \( 150^\circ \) D. \( 60^\circ \) **Graphical Representation:** - The circle is centered at \( O \), with a diameter \( \overline{AB} \). - Radius \( \overline{OC} \) forms a 90-degree angle with \( \overline{AB} \), making \( \overline{OC} \) perpendicular to \( \overline{AB} \). - The angle formed by connecting \( D \rightarrow O \rightarrow C \) is \( 120^\circ \). **Answer the problem by analyzing the angles and relationships within the circle.** --- For more detailed analysis and solution steps, keep visiting our Educational website Tutorials and Geometry sections.
Transcribed Image Text:### Geometry Problem: Angle Determination in a Circle **Problem Statement:** Point \( O \) is the center of the circle. Determine \( m \angle BD \). **Diagram Explanation:** The given diagram is a circle with center \( O \). The circle has four labeled points on its circumference: \( A \), \( B \), \( C \), and \( D \). The points are positioned such that: - \( \angle AOB \) is a straight line passing through the center \( O \). - \( \overline{OC} \) is a radius that forms a right angle (\(90^\circ\)) with \( \overline{AB} \). - There is an angle \( \angle DOC \) marked as \( 120^\circ \). **Options:** A. \( 120^\circ \) B. \( 90^\circ \) C. \( 150^\circ \) D. \( 60^\circ \) **Graphical Representation:** - The circle is centered at \( O \), with a diameter \( \overline{AB} \). - Radius \( \overline{OC} \) forms a 90-degree angle with \( \overline{AB} \), making \( \overline{OC} \) perpendicular to \( \overline{AB} \). - The angle formed by connecting \( D \rightarrow O \rightarrow C \) is \( 120^\circ \). **Answer the problem by analyzing the angles and relationships within the circle.** --- For more detailed analysis and solution steps, keep visiting our Educational website Tutorials and Geometry sections.
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