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Find the missing information for both parts below. (a) In the figure below, m A B = 170° and m A C=68°. Find MZADC. m ZADC = C D A (b) In the figure below, mZ CED=93° and m AB=93°. Find m CD. A m CD =

Find the missing information for both parts below. (a) In the figure below, m A B = 170° and m A C=68°. Find MZADC. m ZADC = C D A (b) In the figure below, mZ CED=93° and m AB=93°. Find m CD. A m CD =

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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The image contains two geometry problems involving circles. 1. **Part (b):** - **Description:** The problem presents a circle with five labeled points: A, B, C, D, and E. The points A, B, C, and D are on the circumference, while point E is inside the circle, with line segments AE, BE, CE, and DE connecting to the circumference. - **Given Angles:** - \( m \angle CED = 93^\circ \) - \( m \overset{\frown}{AB} = 93^\circ \) - **Task:** Find the measure of arc \( \overset{\frown}{CD} \). This problem likely involves properties of circles, such as angles subtended by arcs at the center or from the circumference, as well as the sum of arcs and angles around a point. Understanding these properties will help in solving for the unknown arc \( \overset{\frown}{CD} \).
Transcribed Image Text:The image contains two geometry problems involving circles. 1. **Part (b):** - **Description:** The problem presents a circle with five labeled points: A, B, C, D, and E. The points A, B, C, and D are on the circumference, while point E is inside the circle, with line segments AE, BE, CE, and DE connecting to the circumference. - **Given Angles:** - \( m \angle CED = 93^\circ \) - \( m \overset{\frown}{AB} = 93^\circ \) - **Task:** Find the measure of arc \( \overset{\frown}{CD} \). This problem likely involves properties of circles, such as angles subtended by arcs at the center or from the circumference, as well as the sum of arcs and angles around a point. Understanding these properties will help in solving for the unknown arc \( \overset{\frown}{CD} \).
## Problem Description **Objective:** Find the missing information for both parts below. --- ### Part (a) **Given:** - In the figure below, \(m \overset{\frown}{AB} = 170^\circ\) and \(m \overset{\frown}{AC} = 68^\circ\). **Required:** - Find \(m \angle ADC\). **Diagram Explanation:** - The diagram shows a circle with a secant line that intersects the circle, creating two arcs: \( \overset{\frown}{AB} \) and \( \overset{\frown}{AC} \). - Point A and point D are on the secant line outside the circle, while points B and C are on the circle. --- ### Part (b) **Given:** - In the figure below, \(m \angle CED = 93^\circ \) and \(m \overset{\frown}{AB} = 93^\circ\). **Required:** - Find \(m \overset{\frown}{CD}\). **Diagram Explanation:** - The diagram shows a circle with a chord \(AB\) and another chord \(CD\). - The angle \( \angle CED \) is outside the circle, intercepting arcs \( \overset{\frown}{AB} \) and \( \overset{\frown}{CD} \). - Point E is outside the circle, with the secant line cutting the circle at points C and D. --- This problem involves understanding circle theorems and the relationships between angles and intercepted arcs.
Transcribed Image Text:## Problem Description **Objective:** Find the missing information for both parts below. --- ### Part (a) **Given:** - In the figure below, \(m \overset{\frown}{AB} = 170^\circ\) and \(m \overset{\frown}{AC} = 68^\circ\). **Required:** - Find \(m \angle ADC\). **Diagram Explanation:** - The diagram shows a circle with a secant line that intersects the circle, creating two arcs: \( \overset{\frown}{AB} \) and \( \overset{\frown}{AC} \). - Point A and point D are on the secant line outside the circle, while points B and C are on the circle. --- ### Part (b) **Given:** - In the figure below, \(m \angle CED = 93^\circ \) and \(m \overset{\frown}{AB} = 93^\circ\). **Required:** - Find \(m \overset{\frown}{CD}\). **Diagram Explanation:** - The diagram shows a circle with a chord \(AB\) and another chord \(CD\). - The angle \( \angle CED \) is outside the circle, intercepting arcs \( \overset{\frown}{AB} \) and \( \overset{\frown}{CD} \). - Point E is outside the circle, with the secant line cutting the circle at points C and D. --- This problem involves understanding circle theorems and the relationships between angles and intercepted arcs.
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