Page 147 - Mathematics_Form_3

Circles

Activity 5.10: Examining the Theorem 5.6
properties of a perpendicular A perpendicular bisector of a chord
bisector of a chord passes through the centre of the

circle. The theorem is referred to as
Individually or in a group, perform the
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following tasks: “perpendicular bisector of a chord”.
1. Use a pair of compasses to draw a
circle of a convenient radius with
Theorem 5.6 is described geometrically
the centre O.
as follows.
2. Draw a chord PQ anywhere across
the circle. In Figure 5.17, O is the centre of the

3. Draw the perpendicular bisector of circle, PQ is a chord and MO is the
chord PQ at point R. perpendicular bisector of the chord PQ.

4. Use a ruler to measure the length ‾ PR
and ‾ QR .
5. What is the relationship between
the lengths ‾ PR and ‾ QR ? O
6. Does the perpendicular bisector of
a chord pass through the centre?

7. Write a general statement which
summarizes your observations. P M Q

8. Prove the findings in task 7 Figure 5.17: Perpendicular bisector of a
using the knowledge of algebra,
Mathematics for Secondary Schools In Activity 5.10, you were able to deduce bisector must pass through the centre of
chord
congruence of polygons, similarity,
and other methods of your choice. Theorem 5.6 states that, the perpendicular

9. Share your findings with other
students for further discussion.
the circle as seen in Figure 5.17.

Example 5.17

that when a chord of a circle is bisected
that O is the centre of a circle, ‾ OE = 5 cm,
by a line, its perpendicular bisector
and ‾ OD = 13 cm.
always passes through the centre of the Find the length of the chord CD given
circle. This observation is summarized
in the following theorem.

140 Student\s Book Form Three

18/09/2025 09:59:46
MATHEMATIC F3 SB.indd 140
MATHEMATIC F3 SB.indd 140 18/09/2025 09:59:46