MAJOR ARC
Definition Of Major Arc
Major Arc is the larger of the two arcs formed when a circle is divided into two unequal parts.
More About Major Arc
The measure of major arc is always more than 180° or π radian.
The sum of the measures of the major arc and the minor arc is equal to 360° or 2π radian.
Examples of Major Arc
Arc ABC is a major arc, as the measure of arc ABC is greater than 180°.
Video Examples: *Given CA, Find Intercepted Arc, Major Arc, Inscribed Angle
Solved Example on Major Arc
Ques: Identify an arc that represents a major arc in the circle shown.
Choices:
A. Arc PQR
B. Arc OPS
C. Arc PSR
D. Arc OQR
Correct Answer: A
Solution:
Step 1: An arc of measure greater than 180 degrees is the major arc.
Step 2: In the figure, arc PQR measures greater than 180 degrees. So, arc PQR is the major arc in the circle.
Quick Summary
- The measure of a major arc is always more than 180° or π radians.
- The sum of the measures of the major arc and the minor arc is equal to 360° or 2π radians.
🍎 Teacher Insights
Use visual aids and real-world examples (like pizza slices) to help students differentiate between major and minor arcs. Emphasize the relationship between central angles and intercepted arcs.🎓 Prerequisites
- Circles
- Arcs
- Central Angles
- Degrees
- Radians
Check Your Knowledge
Q1: Which of the following is a major arc?
Q2: If a minor arc measures 75 degrees, what is the measure of its corresponding major arc?
Frequently Asked Questions
Q: How do I identify a major arc?
A: A major arc is an arc whose measure is greater than 180 degrees (or π radians).
Q: How do I calculate the measure of a major arc?
A: If you know the measure of the corresponding minor arc or central angle, subtract that measure from 360 degrees (or 2π radians).