In Figure 2, AC is a diameter. is a semicircle.
Figure 2 A diameter of a circle and a semicircle.
In Figure 3, is a minor arc of circle P.
Figure 3 A minor arc of a circle.
In Figure 4, is a major arc of circle Q.
Figure 4 A major arc of a circle.
Arcs are measured in three different ways. They are measured in degrees and in unit length as follows:
- Degree measure of a semicircle: This is 180°. Its unit length is half of the circumference of the circle.
- Degree measure of a minor arc: Defined as the same as the measure of its corresponding central angle. Its unit length is a portion of the circumference. Its length is always less than half of the circumference.
- Degree measure of a major arc: This is 360° minus the degree measure of the minor arc that has the same endpoints as the major arc. Its unit length is a portion of the circumference and is always more than half of the circumference.
In these examples, m indicates the degree measure of arc AB, l indicates the length of arc AB, and indicates the arc itself.
Example 1: In Figure 5, circle O, with diameter AB has OB = 6 inches. Find (a) m and (b) l .