CENTRAL ANGLE
Definition Of Central Angle
The angle in a circle whose vertex is the center of the circle is called the Central Angle.
Example of Central Angle
In the figure shown, O is the center of the circle and angle POQ is the central angle.
Video Examples: Inscribed and Central Angles
Solved Example onCentral Angle
Ques: A circle is divided into 4 congruent sectors and then each of them is divided into 3 congruent sectors as in the figure. What is the measure of the central angle POQ in degrees?
Choices:
A. 45
B. 30
C. 90
D. 60
Correct Answer: D
Solution:
Step 1: Central angle of each sector = (360/12)° = 30°
Step 2: Measure of the central angle POQ is 2(30) = 60.
Quick Summary
- A central angle has its vertex at the center of the circle.
- The measure of a central angle is equal to the measure of its intercepted arc.
🍎 Teacher Insights
Use visual aids and real-world examples to help students understand the concept of central angles. Emphasize the relationship between central angles and intercepted arcs.🎓 Prerequisites
- Basic angle concepts
- Circle properties
- Understanding of degrees
Check Your Knowledge
Q1: If a circle is divided into 12 congruent sectors, what is the measure of the central angle of each sector?
Frequently Asked Questions
Q: What is the difference between a central angle and an inscribed angle?
A: A central angle has its vertex at the center of the circle, while an inscribed angle has its vertex on the circle.
Q: How do you find the measure of a central angle?
A: The measure of a central angle is equal to the measure of its intercepted arc.