Page 137 - Mathematics_Form_3

Circles

5. Draw other four circles of different Q
radii and repeat tasks 1 to 4.

6. Study carefully the results obtained
in task 4 and write a single statement B
FOR ONLINE READING ONLY
O
which summarizes your findings.
7. Use congruence and similarity A
theorems, circle theorems, algebra,
and any other method of your P
choice to prove the findings you
Figure 5.14: A cyclic quadrilateral AQBP
have obtained in task 6.
ˆ
ˆ
8. Write a general statement which In Figure 5.14, AQB and APB are

summarizes your findings. opposite angles in the cyclic quadrilateral.
̂
̂
Likewise, P A Q and P B Q are opposite
9. Share your findings with other angles in the cyclic quadrilateral.
students for further discussion.
According to Theorem 5.3, it implies that
̂
̂
P A Q + P B Q = 180° and
The conclusion you have made in Activity ̂ ̂
A Q B + A P B = 180° .
5.6 is the circle theorem which describes
the relationship between the opposite
Example 5.9
angles in a cyclic quadrilateral. The
opposite angles in a cylic quadrilateral
sum up to 180 degrees. In other words, the Let O be the centre of a circle as shown
opposite angles in a cyclic quadrilateral in the following figure. Find an equation
Mathematics for Secondary Schools Theorem 5.3 P Q x y O R
relating x and y.
are supplementary.

The opposite angles in a cyclic
quadrilateral are supplementary. This
theorem is referred to as “opposite angles
in a cyclic quadrilateral”.

Theorem 5.3 is geometrically described
as follows.
In Figure 5.14, AQBP is a cyclic
quadrilateral inscribed in a circle with
centre O.

130 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 130
MATHEMATIC F3 SB.indd 130 18/09/2025 09:59:41