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Question (41)

QN0036961

41. A triangle circumscribes a circle. If the two segments into which the point of contact divides one side are 8 cm and 6 cm, the tangent lengths from the two adjacent vertices are:

(A) 8 cm and 6 cm
(B) 6 cm and 8 cm
(C) 8 cm and 14 cm
(D) 14 cm and 6 cm

Correct Answer: A

Explanation:

Tangents drawn from the same external point are equal. Therefore, the corresponding tangent lengths are 8 cm and 6 cm.

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Question (42)

QN0036962

42. In a triangle circumscribing a circle, the point of contact divides one side into segments of 7 cm and 5 cm. If the tangent length from the third vertex is 9 cm, the other two sides are:

(A) 12 cm and 14 cm
(B) 16 cm and 14 cm
(C) 12 cm and 16 cm
(D) 14 cm and 16 cm

Correct Answer: B

Explanation:

The two sides are 7 + 9 = 16 cm and 5 + 9 = 14 cm.

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Question (43)

QN0036963

43. A circle touches all four sides of a quadrilateral. If two adjacent sides are 10 cm and 14 cm and one opposite side is 12 cm, the remaining side is:

(A) 8 cm
(B) 10 cm
(C) 12 cm
(D) 16 cm

Correct Answer: A

Explanation:

Sum of opposite sides is equal. Thus 10 + 12 = 14 + x, giving x = 8 cm.

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Question (44)

QN0036964

44. The tangents drawn at the endpoints of a diameter of a circle are:

(A) Perpendicular
(B) Parallel
(C) Coincident
(D) Intersecting at the centre

Correct Answer: B

Explanation:

Both tangents are perpendicular to the same diameter. Therefore, they are parallel.

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Question (45)

QN0036965

45. If a line is tangent to a circle at P and OP is the radius, then for any other point Q on the tangent line:

(A) OQ < OP
(B) OQ = OP
(C) OQ > OP
(D) OQ = 0

Correct Answer: C

Explanation:

OP is the shortest distance from O to the tangent line. Hence OQ > OP for every other point Q.

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Question (46)

QN0036966

46. A circle has radius 6 cm. A chord of a larger concentric circle touches this circle and has length 16 cm. The radius of the larger circle is:

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

Correct Answer: B

Explanation:

Half chord = 8 cm. Larger radius = √(6² + 8²) = 10 cm.

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Question (47)

QN0036967

47. Two parallel tangents are drawn to a circle. A third tangent intersects them at A and B, with C as its point of contact. If O is the centre, then ∠AOB is:

(A) 45°
(B) 60°
(C) 90°
(D) 180°

Correct Answer: C

Explanation:

For two parallel tangents intersected by a third tangent, the angle subtended by the third tangent segment at the centre is 90°.

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Question (48)

QN0036968

48. In a quadrilateral circumscribing a circle, one pair of opposite sides has total length 25 cm. The total length of the other pair of opposite sides is:

(A) 20 cm
(B) 25 cm
(C) 30 cm
(D) 50 cm

Correct Answer: B

Explanation:

In a tangential quadrilateral, the sums of lengths of opposite sides are equal.

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Question (49)

QN0036969

49. A chord of a circle of radius 25 cm is 7 cm from the centre. Its length is:

(A) 24 cm
(B) 36 cm
(C) 48 cm
(D) 50 cm

Correct Answer: C

Explanation:

Half chord = √(25² − 7²) = √576 = 24 cm. Therefore, chord = 48 cm.

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Question (50)

QN0036970

50. A circle has radius 15 cm. A chord is at a distance of 9 cm from the centre. The length of the chord is:

(A) 12 cm
(B) 18 cm
(C) 24 cm
(D) 30 cm

Correct Answer: C

Explanation:

Half chord = √(15² − 9²) = √144 = 12 cm. Therefore, chord = 24 cm.

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Question (41)

41. A triangle circumscribes a circle. If the two segments into which the point of contact divides one side are 8 cm and 6 cm, the tangent lengths from the two adjacent vertices are:

Explanation:

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Question (42)

42. In a triangle circumscribing a circle, the point of contact divides one side into segments of 7 cm and 5 cm. If the tangent length from the third vertex is 9 cm, the other two sides are:

Explanation:

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Question (43)

43. A circle touches all four sides of a quadrilateral. If two adjacent sides are 10 cm and 14 cm and one opposite side is 12 cm, the remaining side is:

Explanation:

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Question (44)

44. The tangents drawn at the endpoints of a diameter of a circle are:

Explanation:

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Question (45)

45. If a line is tangent to a circle at P and OP is the radius, then for any other point Q on the tangent line:

Explanation:

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Question (46)

46. A circle has radius 6 cm. A chord of a larger concentric circle touches this circle and has length 16 cm. The radius of the larger circle is:

Explanation:

Link:

Question (47)

47. Two parallel tangents are drawn to a circle. A third tangent intersects them at A and B, with C as its point of contact. If O is the centre, then ∠AOB is:

Explanation:

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Question (48)

48. In a quadrilateral circumscribing a circle, one pair of opposite sides has total length 25 cm. The total length of the other pair of opposite sides is:

Explanation:

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Question (49)

49. A chord of a circle of radius 25 cm is 7 cm from the centre. Its length is:

Explanation:

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Question (50)

50. A circle has radius 15 cm. A chord is at a distance of 9 cm from the centre. The length of the chord is:

Explanation:

Link:

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