Page 128 - Mathematics_Form_3

Circles

Angle properties of circles Activity 5.4: Deducing the
Angles formed in a circle under certain relationship between a central
specific conditions are uniquely related. angle and the angle subtended
These relationships are summarized in at the circumference of a circle
general rules known as theorems. by an arc
FOR ONLINE READING ONLY
Individually or in a group, perform the
Relationship between the central
angle and the angle subtended at the following tasks:
circumference of a circle by an arc 1. Use an electronic geoboard or one
In Figure 5.7, APB and AXQYB are two prepared from locally available
arcs of a circle with centre at O. The materials. Prepare a geoboard by
placing nails 1 cm apart on a hard
diameter ‾ XY divides the circle into two board or a piece of flat wood of
equal arcs, XQY and XAPBY. 30 cm by 30 cm that appears as
shown in Figure 5.8.

Figure 5.8: Picture of a geoboard
Figure 5.7: Angle subtended at the centre
and at the circumference of a 2. Use rubber bands to form shapes
on the geoboard as shown in Figure
circle
5.9.
The arc APB subtends an angle AOB
at the centre and angle AQB at the
circumference. Similarly, arc AXQYB Mathematics for Secondary Schools
subtends the reflex angle AOB at the centre
and angle APB at the circumference.
Thus, the angles AOB and AQB, and
reflex angle AOB and angle APB have a
unique relationship. Engage in Activity
5.4 to learn the relationship between the Figure 5.9: Angles formed at the centre
central angle and the angle subtended at and on the circumference of
the circumference of a circle by an arc. a circle

Student\s Book Form Three 121

18/09/2025 09:59:37
MATHEMATIC F3 SB.indd 121 18/09/2025 09:59:37
MATHEMATIC F3 SB.indd 121