Page 146 - Mathematics_Form_3

Circles

5. A boat moves on a circular path 3. Study carefully the two segments
centred at point O, with a lighthouse formed by the folding line.
at A and another at B, forming a 4. How similar or dissimilar are the
diameter of 200 metres. If the boat
two segments of the circle?
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is at a point C on the circumference
5. What can you say about the folding
and 120 metres from A, find the
distance from the boat to point B. line you observed in task 3?
6. What is the name of the folding
line you observed in task 3?
Chord properties of circles
7. Briefly describe the relationship
Like in the case of angles, chords of between the line of symmetry and
circles have unique characteristics a diameter of the circle.
under some conditions. In this section, 8. Share your findings with other
the properties of lines of symmetry of
students for further discussion.
circles, perpendicular bisector of a chord,
parallel chords, and equal chords are
From Activity 5.9, you may have noticed
explored.
that the diameter of a circle is closely
related to its line of symmetry. In fact,
Properties of lines of symmetry of a
every diameter is a line of symmetry and
circle
every line of symmetry passes through
Regular figures are symmetrical.
the centre of a circle is a diameter. This
Symmetry generally refers to an exact
means that a circle has infinitely many
correspondence between opposite halves
lines of symmetry.
of a figure. A circle, like any other
regular figure, is symmetrical. Engage
in Activity 5.9 to learn more about the Properties of the perpendicular
symmetry of a circle. bisector of a chord
A perpendicular bisector is a line which
Activity 5.9: Deducing the line of intersects another line perpendicularly
symmetry of a circle and divides it into two equal parts. Mathematics for Secondary Schools
Thus, the perpendicular bisector of a
Individually or in a group, perform the
chord is a line which intersects a chord
following tasks:
perpendicularly and divides it into two
1. Draw a large circle of a convenient
equal parts. Activity 5.10 enables you to
radius on a manila sheet and cut
learn the properties of a perpendicular
out the circle.
bisector of a chord.
2. Fold the circle along a line through
the centre and unfold it.

Student\s Book Form Three 139

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MATHEMATIC F3 SB.indd 139 18/09/2025 09:59:45
MATHEMATIC F3 SB.indd 139