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4. O is the center of the given circle. If mz1 = 72°, and mDC = 34º, find: A) mAB B) mZAOB C) mz2 O E D

4. O is the center of the given circle. If mz1 = 72°, and mDC = 34º, find: A) mAB B) mZAOB C) mz2 O E D

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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**Problem Statement:** 4. O is the center of the given circle. If \( m \angle 1 = 72^\circ \) and \( m \angle DCE = 34^\circ \), find: A) \( m \overset{\frown}{AB} \) B) \( m \angle AOB \) C) \( m \angle 2 \) **Diagram Explanation:** - The diagram features a circle with center O. - Points A, B, C, D, and E form chords and segments within and outside the circle, extending to point F. - \( \angle 1 \) is inscribed in the circle with point O as the vertex. - \( \angle DCE \) is formed by chords within the circle. - There is a line extending from point C through E to an external point F, forming \( \angle 2 \). **Objective:** To find the measures of: - The arc \( \overset{\frown}{AB} \) corresponding to the chord AB. - The central angle \( \angle AOB \). - The external angle \( \angle 2 \) formed outside the circle.
Transcribed Image Text:**Problem Statement:** 4. O is the center of the given circle. If \( m \angle 1 = 72^\circ \) and \( m \angle DCE = 34^\circ \), find: A) \( m \overset{\frown}{AB} \) B) \( m \angle AOB \) C) \( m \angle 2 \) **Diagram Explanation:** - The diagram features a circle with center O. - Points A, B, C, D, and E form chords and segments within and outside the circle, extending to point F. - \( \angle 1 \) is inscribed in the circle with point O as the vertex. - \( \angle DCE \) is formed by chords within the circle. - There is a line extending from point C through E to an external point F, forming \( \angle 2 \). **Objective:** To find the measures of: - The arc \( \overset{\frown}{AB} \) corresponding to the chord AB. - The central angle \( \angle AOB \). - The external angle \( \angle 2 \) formed outside the circle.
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