Page 122 - Mathematics_Form_3

Circles

6. Again, using the same centre of The length of an arc depends also on the
the circle, increase the radius and size of the circle. For example, taking
draw another circle. Repeat this task a central angle of, say 20° , it can be
two times and study the relationship observed that the larger the circle the
between the angle and the arc of the larger is the arc, as shown in Figure 5.3.
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circle. What happens to the angle In this case, arc CD is larger than arc AB.
and the arc when you increase or C
decrease the radius? A

7. What is your conclusion in tasks 5
and 6? Share the results with other O 20º
students for further discussion.
B
D
In addition to what you discovered in Figure 5.3: Relationship between the
Activity 5.2, Figure 5.2 (a) and Figure radius of a circle and the
5.2 (b) show that the length of an arc of length of an arc
a circle is proportional to the measure Arc length of a circle
of the central angle, provided that the The arc length is the distance along
radius of the circle is not changed. the curved line forming part of the
D circumference between two points.
E Activity 5.3 enables you to derive the
formula for the arc length.

A
Activity 5.3: Deducing the formula
O
for arc length of a circle

Individually or in a group, perform the
following tasks:
(a) 1. Draw a circle of convenient radius
F
and draw two radii that intersect at
the centre as shown in Figure 5.4.
C Mathematics for Secondary Schools

O r
l

O
D
(b) r
Figure 5.2: Relationship between a
central angle and length of
an arc Figure 5.4: The arc length l of a circle

Student\s Book Form Three 115

18/09/2025 09:59:34
MATHEMATIC F3 SB.indd 115
MATHEMATIC F3 SB.indd 115 18/09/2025 09:59:34