Page 133 - Mathematics_Form_3

Circles

Relationship between angles formed
P R
in the same segment of a circle
Consider Figure 5.10 which shows a

O circle with centre O . The segment PRQ
FOR ONLINE READING ONLY
of the circle is bounded by the arc PRQ
96º and the chord PQ. Since X, Y, and Z are
̂ ̂
points on the arc PRQ , angles P X Q, P Y Q
Q S and P Z Q are in the same segment PRQ .
̂
Find:
̂
̂
( a) Q P S (b) Q R S R Y
̂
̂
(c) P O Q (d) P R Q
X Z
5. A satellite orbits the earth along
a circular path. If it subtends an
angle of 64 at the centre of the O
o
Earth, what would be the angle
subtended at a ground station on P Q
the earth’s surface?
6. Given two circles of different
radii, can an arc of the same Figure 5.10: Angles formed in the same
length in each circle subtend equal segment of a circle
angles at their respective centres? The angles formed by the same arc
Explain why?
within the segment PRQ have a unique
7. Prove cases II and IV of the angle relationship to each other. Engage in
Mathematics for Secondary Schools figure. Q Perform the following tasks
at centre theorem
Activity 5.5 to study this relationship.
8. Find the value of x in the following

Activity 5.5: Deducing the
relationship between angles
formed in the same segment

O
individually or in a group:

P 24º 100º x 1. Using the geoboard prepared in
Activity 5.4, trace Figure 5.10 by
R using rubber bands.

126 Student\s Book Form Three

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