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Question (21)

QN0036941

21. Two tangents TP and TQ are drawn from an external point T. If ∠PTQ = 90°, then ∠POQ is:

(A) 45°
(B) 60°
(C) 90°
(D) 180°

Correct Answer: C

Explanation:

The angle between two tangents and the central angle are supplementary. Hence ∠POQ = 180° − 90° = 90°.

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Question (22)

QN0036942

22. If two tangents from an external point make an angle of 120°, the angle subtended by the points of contact at the centre is:

(A) 30°
(B) 60°
(C) 90°
(D) 120°

Correct Answer: B

Explanation:

Central angle = 180° − 120° = 60°.

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Question (23)

QN0036943

23. A chord of a circle of radius 10 cm is 12 cm long. The perpendicular distance of the chord from the centre is:

(A) 6 cm
(B) 8 cm
(C) 10 cm
(D) 12 cm

Correct Answer: B

Explanation:

Half chord = 6 cm. Distance = √(10² − 6²) = √64 = 8 cm.

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Question (24)

QN0036944

24. A chord of a circle of radius 13 cm is 10 cm long. The perpendicular distance from the centre to the chord is:

(A) 5 cm
(B) 10 cm
(C) 12 cm
(D) 13 cm

Correct Answer: C

Explanation:

Half chord = 5 cm. Distance = √(13² − 5²) = √144 = 12 cm.

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Question (25)

QN0036945

25. Two concentric circles have radii 10 cm and 6 cm. A chord of the larger circle touches the smaller circle. The length of the chord is:

(A) 8 cm
(B) 12 cm
(C) 16 cm
(D) 20 cm

Correct Answer: C

Explanation:

Half chord = √(10² − 6²) = 8 cm. Therefore, chord = 16 cm.

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Question (26)

QN0036946

26. Two concentric circles have radii 13 cm and 5 cm. A chord of the larger circle touches the smaller circle. Its length is:

(A) 12 cm
(B) 20 cm
(C) 24 cm
(D) 26 cm

Correct Answer: C

Explanation:

Half chord = √(13² − 5²) = 12 cm. Therefore, chord = 24 cm.

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Question (27)

QN0036947

27. A chord of a circle has length 16 cm and the radius is 10 cm. The radius of the concentric circle touched by the chord is:

(A) 4 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm

Correct Answer: B

Explanation:

Half chord = 8 cm. Distance from centre to chord = √(10² − 8²) = 6 cm. Hence the smaller radius is 6 cm.

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Question (28)

QN0036948

28. A chord of a larger circle touches a concentric smaller circle. If the larger radius is 17 cm and the smaller radius is 8 cm, the chord length is:

(A) 15 cm
(B) 30 cm
(C) 32 cm
(D) 34 cm

Correct Answer: B

Explanation:

Half chord = √(17² − 8²) = 15 cm. Therefore, chord = 30 cm.

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Question (29)

QN0036949

29. A tangent at P to a circle with centre O meets a line through O at Q. If OP = 9 cm and OQ = 15 cm, then PQ is:

(A) 6 cm
(B) 9 cm
(C) 12 cm
(D) 18 cm

Correct Answer: C

Explanation:

OP is perpendicular to PQ. Therefore, PQ = √(15² − 9²) = 12 cm.

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Question (30)

QN0036950

30. A tangent from an external point is 20 cm long and the radius of the circle is 21 cm. The distance of the external point from the centre is:

(A) 25 cm
(B) 29 cm
(C) 30 cm
(D) 41 cm

Correct Answer: B

Explanation:

OP² = 20² + 21² = 841. Hence OP = 29 cm.

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Question (21)

21. Two tangents TP and TQ are drawn from an external point T. If ∠PTQ = 90°, then ∠POQ is:

Explanation:

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Question (22)

22. If two tangents from an external point make an angle of 120°, the angle subtended by the points of contact at the centre is:

Explanation:

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Question (23)

23. A chord of a circle of radius 10 cm is 12 cm long. The perpendicular distance of the chord from the centre is:

Explanation:

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Question (24)

24. A chord of a circle of radius 13 cm is 10 cm long. The perpendicular distance from the centre to the chord is:

Explanation:

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Question (25)

25. Two concentric circles have radii 10 cm and 6 cm. A chord of the larger circle touches the smaller circle. The length of the chord is:

Explanation:

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Question (26)

26. Two concentric circles have radii 13 cm and 5 cm. A chord of the larger circle touches the smaller circle. Its length is:

Explanation:

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Question (27)

27. A chord of a circle has length 16 cm and the radius is 10 cm. The radius of the concentric circle touched by the chord is:

Explanation:

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Question (28)

28. A chord of a larger circle touches a concentric smaller circle. If the larger radius is 17 cm and the smaller radius is 8 cm, the chord length is:

Explanation:

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Question (29)

29. A tangent at P to a circle with centre O meets a line through O at Q. If OP = 9 cm and OQ = 15 cm, then PQ is:

Explanation:

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Question (30)

30. A tangent from an external point is 20 cm long and the radius of the circle is 21 cm. The distance of the external point from the centre is:

Explanation:

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