### Extra Example 1Find the measure of each arc of circle $ C $, where $ \overline{AB} $ is a diameter.#### Diagram:- The diagram shows a circle with center $ C $.- The line segment $ \overline{AB} $ is the diameter of the circle.- Point $ D $ is on the circumference of the circle and forms a triangle $ \triangle ADB $ with points $ A $ and $ B $.- The central angle $ \angle ACD $ is given as $ 65^\circ $.#### Tasks:Determine the measure of the following arcs:a. $ \overset{\frown}{AD} $b. $ \overset{\frown}{DAB} $c. $ \overset{\frown}{BDA} $### Explanation of the Diagram:- The circle $ C $ has a diameter $ \overline{AB} $, which means $ \angle ACB = 180^\circ $ since a diameter subtends a semicircle.- The central angle $ \angle ACD $ is given as $ 65^\circ $.- Since $ \overline{AB} $ is a diameter, $ \overline{ACD} $ and $ \overline{BDC} $ are supplementary and add up to the diameter's total of $ 180^\circ $. Hence, arc $ \overset{\frown}{AD} $ is $ 65^\circ $.To find the remaining arcs:- Arc $ \overset{\frown}{BD} $ can be calculated by subtracting $ \overset{\frown}{AD} = 65^\circ $ from $ 180^\circ $, so $ \overset{\frown}{BD} $ is $ 115^\circ $.Given these details, complete the exercises to find the measures of arcs $ AD, DAB, $ and $ BDA $ based on relationships and supplementary angles in the circle.

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Description: ### Extra Example 1Find the measure of each arc of circle $ C $, where $ \overline{AB} $ is a diameter.#### Diagram:- The diagram shows a circle with center $ C $.- The line segment $ \overline{AB} $ is the diameter of the circle.- Point \(

To measure each arc of C as centre and AB as diameter

Answered: Extra Example 1 Find the measure of…

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Extra Example 1 Find the measure of each arc of OC, where AB is a diameter. A 65% а. AD b. DAB С. BDA

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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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

Topic Video

Question

### Extra Example 1

Find the measure of each arc of circle $ C $, where $ \overline{AB} $ is a diameter.

#### Diagram:
- The diagram shows a circle with center $ C $.
- The line segment $ \overline{AB} $ is the diameter of the circle.
- Point $ D $ is on the circumference of the circle and forms a triangle $ \triangle ADB $ with points $ A $ and $ B $.
- The central angle $ \angle ACD $ is given as $ 65^\circ $.

#### Tasks:
Determine the measure of the following arcs:
a. $ \overset{\frown}{AD} $
b. $ \overset{\frown}{DAB} $
c. $ \overset{\frown}{BDA} $

### Explanation of the Diagram:
- The circle $ C $ has a diameter $ \overline{AB} $, which means $ \angle ACB = 180^\circ $ since a diameter subtends a semicircle.
- The central angle $ \angle ACD $ is given as $ 65^\circ $.
- Since $ \overline{AB} $ is a diameter, $ \overline{ACD} $ and $ \overline{BDC} $ are supplementary and add up to the diameter's total of $ 180^\circ $. Hence, arc $ \overset{\frown}{AD} $ is $ 65^\circ $.

To find the remaining arcs:
- Arc $ \overset{\frown}{BD} $ can be calculated by subtracting $ \overset{\frown}{AD} = 65^\circ $ from $ 180^\circ $, so $ \overset{\frown}{BD} $ is $ 115^\circ $.

Given these details, complete the exercises to find the measures of arcs $ AD, DAB, $ and $ BDA $ based on relationships and supplementary angles in the circle.

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