1. In the given figure, AB is a chord of a circle with centre at O. ∠ABT = 80°. Find ∠AOB
2. In the given figure, PQ is the tangent. OQ = 6 cm, OP = 10 cm find PR.
3. In the given figure, OP = diameter, OT is radius, find ∠OPT.
4. From the given figure, AP = 2r find ∠APO.
5. Two circles of radii 8.2 cm and 3.6 cm touch each other externally, the distance between their centres is
(a) 4.6 cm (b) 11.8 cm (c) 4.1 cm (d) 1.8 cm
6. In the diagram if AD = 6 cm, AF = 12 cm, then the length of DE is
(a) 12 cm (b) 24 cm (c) 18 cm (d) 144 cm
7. The length of the tangent from a point at a distance of 13 cm from the centre of the circle of radius 5 cm is
(a) 8 cm (b) 12 cm
(c) 
(d) 1
8.AB and CD are two chords of a circle intersecting at point P inside the circle. If AB = 12 cm, AP = 2 cm, PD = 4 cm, then CP is equal to
(a) 4 cm (b) 2 cm (c) 3 cm (d) 5 cm
9. The perimeter of the quadrilateral APOQ is 26 cm and AP = 10 cm. O is the centre of the circle. Then the radius of the circle is (where AP and AQ are the tangents from A)
(a) 6 cm (b) 3 cm (c) 8 cm (d) 16 cm
10. In the figure, PA and PB are tangents to the circle drawn from an external point P. Also, CD is a tangent to the circle at Q.
If PA = 8 cm and CQ = 3 cm then PC is equal to:
(a) 11 cm (b) 5 cm (c) 24 cm (d) 38 cm
11. In the figure, if ∠PAB = 120° then ∠APT =
(a) 120° (b) 30° (c) 40° (d) 60°
12. If two circles touch internally, then the number of their common tangents is
(a) 2 (b) 1 (c) 4 (d) 3
13. The length of the tangent from a point A to a circle, of radius 3 cm, is 4 cm. The distance (in cm) of A from the centre of the circle is :
(a) √7 (b) 7 (c) 5 (d) 25
14. O is the centre of circle in the given figure, and ∠BDC = 42°, then ∠ACB is equal to :
(a) 42° (b) 48° (c) 45° (d) 60°
15. A line which intersects a circle in two points is called :
(a) Secant (b) Chord
(c) Tangent (d) Diameter
16. Which of the following statements is true for a cyclic quadrilateral?
(a) One of the opposite angles is always obtuse
(b) One of the opposite angles is always acute
(c) Opposite angles are complementary
(d) Opposite angles are supplementary
17. What is the distance between two parallel tangents of a circle of radius 4 cm ?
18. In the given figure, OQ = r = 4 cm
OP = 5 cm find PR.
19. In the given figure, find the length of PR.
20. In the given figure, RQ is tangent with centre at O. If SQ = 8 cm, QR = 3 cm find OR
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