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Question (31)

QN0036951

31. A tangent from an external point has length 12 cm. If the radius is 5 cm, the distance of the point from the centre is:

(A) 7 cm
(B) 13 cm
(C) 17 cm
(D) 144 cm

Correct Answer: B

Explanation:

OP = √(12² + 5²) = √169 = 13 cm.

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Question (32)

QN0036952

32. A tangent from an external point has length 16 cm and the distance of the point from the centre is 20 cm. The radius is:

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

Correct Answer: C

Explanation:

r² = 20² − 16² = 144. Therefore, r = 12 cm.

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Question (33)

QN0036953

33. Two tangents TP and TQ are drawn from T to a circle. If ∠PTQ = 50°, then ∠OPQ is:

(A) 20°
(B) 25°
(C) 40°
(D) 50°

Correct Answer: B

Explanation:

∠OPQ = 90° − (180° − 50°)/2 = 25°.

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Question (34)

QN0036954

34. Two tangents TP and TQ are drawn from T to a circle. If ∠PTQ = 80°, then ∠OPQ is:

(A) 20°
(B) 40°
(C) 50°
(D) 80°

Correct Answer: C

Explanation:

∠OPQ = 90° − (180° − 80°)/2 = 50°.

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Question (35)

QN0036955

35. Two tangents TP and TQ are drawn to a circle. If ∠OPQ = 35°, then ∠PTQ is:

(A) 35°
(B) 70°
(C) 110°
(D) 145°

Correct Answer: B

Explanation:

From the tangent geometry, ∠PTQ = 2∠OPQ = 2 × 35° = 70°.

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Question (36)

QN0036956

36. Two tangents TP and TQ are drawn from T to a circle. If ∠PTQ = 100°, then ∠OPQ is:

(A) 30°
(B) 40°
(C) 50°
(D) 80°

Correct Answer: C

Explanation:

∠OPQ = ½∠PTQ = 50°.

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Question (37)

QN0036957

37. A quadrilateral ABCD circumscribes a circle. If AB = 8 cm, BC = 11 cm and CD = 7 cm, then AD is:

(A) 4 cm
(B) 10 cm
(C) 12 cm
(D) 14 cm

Correct Answer: A

Explanation:

For a tangential quadrilateral, AB + CD = AD + BC. Thus 8 + 7 = AD + 11, giving AD = 4 cm.

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Question (38)

QN0036958

38. A tangential quadrilateral has sides AB = 13 cm, BC = 9 cm and CD = 11 cm. The fourth side AD is:

(A) 5 cm
(B) 11 cm
(C) 13 cm
(D) 15 cm

Correct Answer: D

Explanation:

AB + CD = AD + BC. Therefore 13 + 11 = AD + 9, so AD = 15 cm.

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Question (39)

QN0036959

39. A quadrilateral circumscribes a circle. If three consecutive sides are 7 cm, 12 cm and 9 cm, the fourth side is:

(A) 4 cm
(B) 5 cm
(C) 8 cm
(D) 10 cm

Correct Answer: A

Explanation:

7 + 9 = 12 + AD. Hence AD = 4 cm.

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Question (40)

QN0036960

40. A parallelogram circumscribes a circle. Which conclusion follows?

(A) It is always a rectangle
(B) It is always a rhombus
(C) It is always a square
(D) It is always a trapezium

Correct Answer: B

Explanation:

In a parallelogram circumscribing a circle, the tangential quadrilateral property makes all four sides equal. Hence it is a rhombus.

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Question (31)

31. A tangent from an external point has length 12 cm. If the radius is 5 cm, the distance of the point from the centre is:

Explanation:

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Question (32)

32. A tangent from an external point has length 16 cm and the distance of the point from the centre is 20 cm. The radius is:

Explanation:

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Question (33)

33. Two tangents TP and TQ are drawn from T to a circle. If ∠PTQ = 50°, then ∠OPQ is:

Explanation:

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Question (34)

34. Two tangents TP and TQ are drawn from T to a circle. If ∠PTQ = 80°, then ∠OPQ is:

Explanation:

Link:

Question (35)

35. Two tangents TP and TQ are drawn to a circle. If ∠OPQ = 35°, then ∠PTQ is:

Explanation:

Link:

Question (36)

36. Two tangents TP and TQ are drawn from T to a circle. If ∠PTQ = 100°, then ∠OPQ is:

Explanation:

Link:

Question (37)

37. A quadrilateral ABCD circumscribes a circle. If AB = 8 cm, BC = 11 cm and CD = 7 cm, then AD is:

Explanation:

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Question (38)

38. A tangential quadrilateral has sides AB = 13 cm, BC = 9 cm and CD = 11 cm. The fourth side AD is:

Explanation:

Link:

Question (39)

39. A quadrilateral circumscribes a circle. If three consecutive sides are 7 cm, 12 cm and 9 cm, the fourth side is:

Explanation:

Link:

Question (40)

40. A parallelogram circumscribes a circle. Which conclusion follows?

Explanation:

Link:

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