Page 151 - Mathematics_Form_3

Circles

B D
2. Draw any two chords PQ and RS
of equal length.

3. Locate the midpoints A and B of the P Q
chords ‾ PQ and ‾ RS , respectively. O
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4. Join ‾ AO and ‾ BO .
A C
5. Using a ruler, measure the lengths
of ‾ AO and ‾ BO .
Figure 5.19: Equal chords
6. What is the relationship between In Figure 5.19, if the chords, AB
the lengths ‾ AO and ‾ BO ?
and CD are equal, then the two
7. Write a general statement which chords must be separated by the same
summarizes your observation in perpendicular distance from the centre.
task 6. In this case, since ‾ AB = ‾ CD, it implies

that ‾ OP = ‾ OQ .
8. Use the concepts of congruence of
polygons, similarity, algebra, and
previous circle theorems to prove Example 5.19
your conclusion in task 7. In the following figure, XY and PQ
are parallel chords in a circle with
9. Share your findings with other
centre O and radius 5 cm. If XY = 8
students for further discussion.
cm and PQ = 4 cm, find the distance
between the chords.
From Activities 5.11 and 5.12, you might
have discovered that chords with the P N Q
Mathematics for Secondary Schools observation is explained in Theorem 5.8. X M O Y
same length are separated by the same
distance from the centre of a circle. This

Theorem 5.8
Equal chords of a circle are equidistant
from the centre, this theorem is
referred to as “equal chords”.

The distance between the chord is MN.
Theorem 5.8 is described geometrically
as follows. Solution
Construction: In the figure, the two
In Figure 5.19, O is the centre of the parallel chords are on either side of the
circle. centre O . So that ‾ OM is perpendicular

144 Student\s Book Form Three

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