A chord of a circle divides the circle into two regions,
which are called the segments of the circle.
The minor segment is the region bounded by the chord and the
minor arc intercepted by the chord.
The major segment is the region bounded by the chord and the
major arc intercepted by the chord.
Angles in Different Segments
Angles in the Same Segment
Theorem
Use the information given in the diagram to prove that the angles in
the same segment of a circle are
equal. That is, a = b.
Given:
To prove:
Construction:
Join O to A and B.
Proof:
In general:
Angles in the same segment of a circle are equal.
Practical applications
Danger Angle
If there are rocks near the shore, then boats are informed by the chart
(map) to keep the angle subtended by two land marks, A and B,
smaller than the given danger angle.
Angle for Scoring a Goal in Soccer
All positions on the same arc of a circle give the same angle for
scoring a goal in soccer. Note that the distance of the shot changes but
the angle of possible shots remains constant.
Example 25
Find the value of the pronumeral in the following circle centred at O.
Solution:
Example 26
Find the value of each of the pronumerals in the following circle centred at O.
Solution:
Example 27
Find the value of each of the pronumerals in the following circle centred at O:
