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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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find the measure of BAC
### Geometry Problem: Angle Measurement in a Circle #### Problem Statement: Given a circle with center \( O \), three points \( A \), \( B \), and \( C \) lie on the circumference of the circle. The angle at the center formed by the lines \( OB \) and \( OC \) measures \( 69^\circ \). #### Task: Find the measure of \( \angle BAC \). #### Diagram Explanation: - The circle has a designated center denoted by the point \( O \). - Points \( A \), \( B \), and \( C \) are positioned on the circumference of the circle. - Line segments \( OB \) and \( OC \) form an angle at the center, specifically an angle of \( 69^\circ \). The angles subtended at the center of a circle are twice the angles subtended at the circumference. Thus, the measure of \( \angle BAC \) can be found using the relationship: \[ \angle BAC = \frac{1}{2} \times \angle BOC \] By substituting the given value: \[ \angle BAC = \frac{1}{2} \times 69^\circ = 34.5^\circ \] Therefore, the measure of \( \angle BAC \) is \( 34.5^\circ \).
Transcribed Image Text:### Geometry Problem: Angle Measurement in a Circle #### Problem Statement: Given a circle with center \( O \), three points \( A \), \( B \), and \( C \) lie on the circumference of the circle. The angle at the center formed by the lines \( OB \) and \( OC \) measures \( 69^\circ \). #### Task: Find the measure of \( \angle BAC \). #### Diagram Explanation: - The circle has a designated center denoted by the point \( O \). - Points \( A \), \( B \), and \( C \) are positioned on the circumference of the circle. - Line segments \( OB \) and \( OC \) form an angle at the center, specifically an angle of \( 69^\circ \). The angles subtended at the center of a circle are twice the angles subtended at the circumference. Thus, the measure of \( \angle BAC \) can be found using the relationship: \[ \angle BAC = \frac{1}{2} \times \angle BOC \] By substituting the given value: \[ \angle BAC = \frac{1}{2} \times 69^\circ = 34.5^\circ \] Therefore, the measure of \( \angle BAC \) is \( 34.5^\circ \).
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