Page 153 - Mathematics_Form_3

Circles

4. 9. In the following figure, O and P are
A 16 B centres of the two circles and ABCD
P
is perpendicular to ‾ OP at X . Prove
6
that ‾ CD = ‾ AB .
O
FOR ONLINE READING ONLY
A
D
x B
Q C
O P
5. Two chords, AB and CDof a circle X
whose radius is 13 cm are equal and C
parallel. If each chord is 12 cm long, D
find the distance between them.

6. Two circles with centres A and 10. In the following figure, O is the
B have radii 13 cm and 10 cm, centre of the circle, DP = 2x cm,

respectively, and intersect at P and BQ =x cm, OP =h cm and OQ =l cm.
Q. If ‾ PQ = 12 cm , find the distance

between the centres, giving your If OP and OQ are perpendicular
answer correct to 1 decimal place. to CD and AB, respectively, show

7. Two circles with centres X and Y that AB = 2 ( 3 l − h 2 ) cm.
2
intersect at R and S. If RS = 24 cm, 3
D
XY = 14 cm and the radius of one
circle is 15 cm, find the radius of 2x
the other circle. P h O x
Mathematics for Secondary Schools and ‾ ON = 4 cm . Show that 11. Prove that, chords which are
8. In the following figure, O is the
l
centre of the circle, ‾ AB = 6 cm ,
A
B
Q
_
‾ = 3 √ 10 cm .
C
AP
P
equidistant from the centre of a
circle are equal in length.

12. If chords subtend equal angles at
O
4 cm
the centre of a circle, prove that, the
A B
N chords are equal.

146 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 146