Page 139 - Mathematics_Form_3

Circles

ˆ
⇒ SVU 55+ ° = 180° 5. Can a quadrilateral be cyclic if one
of its angles is greater than 180°?
ˆ
⇒ SVU 180= °− 55° Explain.

125= ° 6. A boat is traveling along a circular
lake. Four observation towers A,
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ˆ
Therefore, STU 55= ° and B, C, and D are placed at different
ˆ
SVU 125 .= ° points along the shore, forming a
cyclic quadrilateral. If two angles of
Exercise 5.6 the quadrilateral are DAB 4x∠ =
and ∠ BCD = 2x + 60° , find the
1. Let O be the centre of a circle. The value of x and measures of these
points A, B, C, and D are concyclic angles.
forming a cyclic quadrilateral. If
∠ ABC 50= ° and ∠ BCD = 60° , 7. Prove that the opposite angles
determine the measures of BAD∠ of a cyclic quadrilateral are
and CDA.∠ supplementary.

2. In a cyclic quadrilateral ABCD,
∠ DAB 2x= + 14° and Relationship between the interior
∠ BCD 3x= − 16° . Find the value angle in a cyclic quadrilateral and
of x. its opposite exterior angle
You have learnt that the sum of two
3. A quadrilateral ABCD is formed opposite angles of a cyclic quadrilateral
inside a circle. If ABC 3x∠ = + 15° is 180 degrees. The interior angle
9
and ∠ ADC = 2 x − 30° , find the of a cyclic quadrilateral and its

Mathematics for Secondary Schools 4. In the following figure, if O is the Activity 5.7 to study this relationship.
corresponding exterior angle shares a
value of x and the measures of
these angles.
unique relationship as well. Engage in

centre of the circle, find the value
Activity 5.7: Deducing the
of x.
relationship between an interior
angle in a cyclic quadrilateral
and its opposite exterior angle

P
2x O Individually or in a group, perform
the following tasks:
3x 1. Draw a cyclic quadrilateral in a
R
circle of any convenient radius.
Q

132 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 132
MATHEMATIC F3 SB.indd 132 18/09/2025 09:59:42