Page 222 - ICSE Math 8

PRACTICE TIME

1. In a circle of radius 7 cm, can we draw a chord of length 15 cm? Justify.
2. If the radius of a circle with centre O is 10 cm, find whether points D, E, F lie inside, outside or on the
circle if:
(a) OD = 12 cm (b) OE = 10 cm (c) OF = 7 cm

3. Two tangents AB and AC are drawn to a circle with centre O from
an external point A. Prove that ∠BAC = 2∠OBC.

4. PQRS is a quadrilateral drawn to circumscribe a circle.
Prove that PQ + RS = PS + QR.

5. Draw a circle of radius 5 cm with centre O. Draw radii OP and OQ such that ∠POQ = 60°. Join PQ.
Find the length of PQ.

6. In the given figure, PQ is a tangent from external point P to the
circle with centre O. If PQ = 8 cm and OP = 10 cm, find the radius
of the circle.

7. In each of the following figures, O is the centre of the circle. Find the values of angles x and y.

(a) (b) (c) (d) A
x 12 cm
O y O x
x 120° C y cm O
y 35° y
x cm 5 cm
B
8. Find the length of a tangent drawn to a circle of radius 8 cm from a point 17 cm from the centre.

P
3 cm
S
9. In the given figure, PQ, QR and PR are tangents to the circle
with centre O. If PS = 3 cm, QT = 4 cm and RU = 5 cm, find Q O U
the perimeter of triangle PQR. 4 cm
T 5 cm

R
B

10. In the adjoining figure, AB is a tangent to a circle with centre O. O 120° A
If ∠BCA = 120°, find ∠CBA. C

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