The radian measure of the central angle is .
Further explanation:
In the question it is given that the length of the arc CD is of the circumference of a circle.
Consider a circle of radius so, the circumference of the circle is .
Step 1: Obtain the length of the arc
The length of the arc CD is of the circumference of the circle.
The length of the arc CD is calculated as follows:
Therefore, the length of the arc CD is units.
Step 2: Obtain the central angle of the arc in degree
The central angle for a circle of circumference of is .
The central angle for an arc CD is calculated as follows:
This implies that the central angle of the arc CD is .
Step 3: Obtain the central angle of the arc in radian
Radian is defined as an angle which is subtended by an arc at the center such that the length of an arc is equal to the radius of the circle.
The measure of angle in terms of radians is so, the measure of angle in terms of radians is .
The central angle for an arc CD is calculated as follows:
Therefore, the radian measure of the central angle is .
Learn more:
1. A problem on composite function brainly.com/question/2723982
2. A problem to find radius and center of circle brainly.com/question/9510228
3. A problem to determine intercepts of a line brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Circle
Keywords: Circle, arc, radian, degree, central angle, circumference, length of arc, measure, circumference, angle, 360 degree, 2pir, radius, diameter.