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Question (11)

QN0036931

11. A circle has radius 7 cm. From an external point, the distance to the centre is 25 cm. The length of the tangent is:

(A) 18 cm
(B) 24 cm
(C) 25 cm
(D) 32 cm

Correct Answer: B

Explanation:

By Pythagoras, tangent² = 25² − 7² = 576. Therefore tangent = 24 cm.

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Question (12)

QN0036932

12. A tangent from a point P to a circle is 15 cm long. If OP = 17 cm, where O is the centre, the radius is:

(A) 6 cm
(B) 7 cm
(C) 8 cm
(D) 9 cm

Correct Answer: C

Explanation:

r² = OP² − PT² = 17² − 15² = 64. Hence r = 8 cm.

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Question (13)

QN0036933

13. A tangent of length 24 cm is drawn from a point whose distance from the centre is 26 cm. The radius of the circle is:

(A) 8 cm
(B) 10 cm
(C) 12 cm
(D) 14 cm

Correct Answer: B

Explanation:

r² = 26² − 24² = 100. Therefore r = 10 cm.

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Question (14)

QN0036934

14. The distance of an external point from the centre of a circle is 13 cm and the radius is 5 cm. The tangent length is:

(A) 8 cm
(B) 10 cm
(C) 12 cm
(D) 18 cm

Correct Answer: C

Explanation:

PT² = 13² − 5² = 144. Therefore PT = 12 cm.

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Question (15)

QN0036935

15. A circle has radius 9 cm and an external point is 41 cm from its centre. The tangent length is:

(A) 32 cm
(B) 36 cm
(C) 40 cm
(D) 42 cm

Correct Answer: C

Explanation:

PT = √(41² − 9²) = √1600 = 40 cm.

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Question (16)

QN0036936

16. Tangents PA and PB are drawn from an external point P. If PA = 3x + 2 and PB = 5x − 10, then x is:

(A) 4
(B) 5
(C) 6
(D) 8

Correct Answer: C

Explanation:

PA = PB, so 3x + 2 = 5x − 10. Hence 2x = 12 and x = 6.

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Question (17)

QN0036937

17. Tangents PA and PB from P have lengths 2x + 5 cm and 4x − 9 cm. Their common length is:

(A) 17 cm
(B) 18 cm
(C) 19 cm
(D) 20 cm

Correct Answer: C

Explanation:

Since PA = PB, 2x + 5 = 4x − 9, giving x = 7. Common length = 19 cm.

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Question (18)

QN0036938

18. Two tangents from an external point make an angle of 70° with each other. The angle subtended by the line joining the points of contact at the centre is:

(A) 70°
(B) 90°
(C) 110°
(D) 140°

Correct Answer: C

Explanation:

The angle between two tangents and the angle subtended at the centre are supplementary. Therefore, 180° − 70° = 110°.

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Question (19)

QN0036939

19. Two tangents from an external point are inclined at 80°. The angle subtended by the line joining the points of contact at the centre is:

(A) 80°
(B) 90°
(C) 100°
(D) 120°

Correct Answer: C

Explanation:

Required angle = 180° − 80° = 100°.

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Question (20)

QN0036940

20. If the angle between two tangents from an external point is 60°, then each of the equal angles made by the line joining the external point to the centre with the tangents is:

(A) 30°
(B) 45°
(C) 60°
(D) 90°

Correct Answer: C

Explanation:

The angle at the centre is 180° − 60° = 120°. The remaining two equal angles are (180° − 120°)/2 = 30°. Therefore, the angle made by the centre line with either tangent is 60° because the radius is perpendicular to the tangent.

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Question (11)

11. A circle has radius 7 cm. From an external point, the distance to the centre is 25 cm. The length of the tangent is:

Explanation:

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Question (12)

12. A tangent from a point P to a circle is 15 cm long. If OP = 17 cm, where O is the centre, the radius is:

Explanation:

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Question (13)

13. A tangent of length 24 cm is drawn from a point whose distance from the centre is 26 cm. The radius of the circle is:

Explanation:

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Question (14)

14. The distance of an external point from the centre of a circle is 13 cm and the radius is 5 cm. The tangent length is:

Explanation:

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Question (15)

15. A circle has radius 9 cm and an external point is 41 cm from its centre. The tangent length is:

Explanation:

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Question (16)

16. Tangents PA and PB are drawn from an external point P. If PA = 3x + 2 and PB = 5x − 10, then x is:

Explanation:

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Question (17)

17. Tangents PA and PB from P have lengths 2x + 5 cm and 4x − 9 cm. Their common length is:

Explanation:

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Question (18)

18. Two tangents from an external point make an angle of 70° with each other. The angle subtended by the line joining the points of contact at the centre is:

Explanation:

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Question (19)

19. Two tangents from an external point are inclined at 80°. The angle subtended by the line joining the points of contact at the centre is:

Explanation:

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Question (20)

20. If the angle between two tangents from an external point is 60°, then each of the equal angles made by the line joining the external point to the centre with the tangents is:

Explanation:

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