Page 135 - Mathematics_Form_3

Circles

ˆ
Example 5.7 Thus, PRQ 180= °− 122°
Triangles ACD and BCD are inscribed = 58°
ˆ
in a circle in which BD is a diameter Therefore, PRQ 58 .= °
and DC is a chord. If CAD∠ = 4x +°
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and CBD 5x∠ = − 10° , find the value of Exercise 5.5
x and measures of these angles. 1. Given a circle with centre O,
Solution chord AB that subtends an
4x + 5° = 5x − 10° (angles in the angle ACB∠ at a point C on the
same segment) circumference. Another point D
5x − 4x = 10°+ 5° on the same segment is such that
x
⇒= 15° ∠ ADB = x . If ACB 50∠ = ° , find
Substituting the value of x gives, the value of x.
4 15×
∠ ACB = ∠4x ACB 4x=5+° = 4× +°15 5 =5°+° °+° 2. In a circle, the chord XY subtends
5
60= °+ 5° angles XPY∠ and XQY∠ at points
65= ° P and Q, respectively, in the same
Therefore, ACB∠ = ∠ ADB 65 .= ° segment. If XPY∠ = 3x + 10° and
∠ XQY = 4x − 20° . Find the value
of x and the measures of XPY∠
Example 5.8
and XQY∠ .
In the following figure, find the size 3. Two chords AB and CD of a
ˆ
of PRQ. circle with the same length subtend
Q angles of 2x +° and 3x − 10° at
5
54° the circumference. Find the value
of x and the measure of each angle.
Mathematics for Secondary Schools Solution ˆ ° (angles in the S
4. Study the following figure and
R
answer the question that follows.
P
80°
32°
T

From the given figure, it implies that
ˆ
PQT 54=
PRT =
same segment)
ˆ
TRS 180=
°−
32 ) 68° =
°
(80°+
(sum of interior angles of a triangle) i O
ˆ
54°+ 68°+ PRQ 180= °
(degree measure of straight angle)

128 Student\s Book Form Three

18/09/2025 09:59:40
MATHEMATIC F3 SB.indd 128 18/09/2025 09:59:40
MATHEMATIC F3 SB.indd 128