Page 149 - Mathematics_Form_3

Circles

Exercise 5.9
5. In the following figure, the line PA
1. Given a circle with centre O, a chord is a diameter of a circle with centre
CD of length 12 cm is bisected O. Chord WE is perpendicular to
perpendicularly by a line passing
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through O. If the perpendicular PA at C. The radius OP 10cm,=
bisector meets CD at point N, find OC = 4 OA. Calculate the length
the radius of the circle given that 5
ON 5cm= . PW.

2. In the following figure, C, D, E, and W
F are points on a circle with centre
O. A chord CE is perpendicular to C
P A
the diameter DF at G. If DG = 2cm O 6 cm

ˆ
and EFG = 30 ,° Calculate the length
E
EG .
6. A chord of length (2x + 4) cm is
C
D bisected perpendicularly. The
2 cm radius of the circle is 5x cm, and

G the perpendicular bisector is 3x cm
O from the centre. Find the value of x.
30 E 7. Prove that, a line joining the
F centre to the midpoint of a chord
Mathematics for Secondary Schools 4. A circular park has a walking path they extend. Parallel chords have the
is perpendicular to the chord.
3. In a circle with centre O, a chord AB
is bisected at M by a perpendicular
line through O. If AB 18cm=
and
Properties of parallel chords of a circle
the radius is 10 cm, find the distance
Parallel lines are lines which are
from O to AB.
separated by a constant distance as
same feature, they are separated by a
in the form of a chord of 40 m. The
perpendicular distance from the
this property, parallel chords of a circle
centre to the path is 9 m. Find the
have unique properties as revealed in
radius of the park. constant distance between them. Due to
Activity 5.11.

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