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Question (21)

QN009438

In a circle of radius 15 cm, a chord is 9 cm away from the centre. The chord length is:

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

Correct Answer: C

Explanation:

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

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Question (22)

QN009439

If two points on a circle subtend equal angles at two other points lying on the same side of the chord, then the four points are:

(A) Collinear
(B) Equidistant
(C) Concyclic
(D) Parallel

Correct Answer: C

Explanation:

Equal subtended angles imply concyclic points.

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Question (23)

QN009440

A diameter AB of a circle subtends angle ACB at point C on the circle. If ∠CAB = 35°, then ∠CBA is:

(A) 35°
(B) 45°
(C) 55°
(D) 90°

Correct Answer: C

Explanation:

∠ACB = 90°, so ∠CBA = 55°.

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Question (24)

QN009441

The perpendicular bisector of any chord of a circle always passes through:

(A) Midpoint of radius
(B) Circumference
(C) Centre of the circle
(D) Tangent point

Correct Answer: C

Explanation:

Perpendicular bisector of a chord passes through the centre.

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Question (25)

QN009442

In a circle, two chords are at distances 3 cm and 5 cm from the centre. Which chord is longer?

(A) Chord at 5 cm
(B) Chord at 3 cm
(C) Both equal
(D) Cannot be determined

Correct Answer: B

Explanation:

Chord nearer to centre is longer.

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Question (26)

QN009443

A chord subtends an angle of 150° at the centre. The angle subtended at the circumference in the same segment is:

(A) 30°
(B) 60°
(C) 75°
(D) 150°

Correct Answer: C

Explanation:

Angle at circumference = 150°/2 = 75°.

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Question (27)

QN009444

In a circle, if two chords are equidistant from the centre, then they are:

(A) Perpendicular
(B) Equal
(C) Diameters
(D) Tangents

Correct Answer: B

Explanation:

Equidistant chords are equal.

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Question (28)

QN009445

A circle has radius 17 cm. A chord is 8 cm from the centre. The length of the chord is:

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

Correct Answer: B

Explanation:

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

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Question (29)

QN009446

If a chord subtends equal angles at two different points on the same segment of a circle, then the points and endpoints of the chord form:

(A) A rectangle
(B) A trapezium
(C) A cyclic quadrilateral
(D) A rhombus

Correct Answer: C

Explanation:

Equal angles in same segment imply cyclic quadrilateral.

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Question (30)

QN009447

A wheel has spokes connected to two points on its rim by a tight string. When the wheel rotates, the angle subtended by the string at the centre:

(A) Changes continuously
(B) Becomes zero
(C) Remains same
(D) Doubles

Correct Answer: C

Explanation:

Rotation does not change the subtended angle.

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Question (21)

In a circle of radius 15 cm, a chord is 9 cm away from the centre. The chord length is:

Explanation:

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Question (22)

If two points on a circle subtend equal angles at two other points lying on the same side of the chord, then the four points are:

Explanation:

Link:

Question (23)

A diameter AB of a circle subtends angle ACB at point C on the circle. If ∠CAB = 35°, then ∠CBA is:

Explanation:

Link:

Question (24)

The perpendicular bisector of any chord of a circle always passes through:

Explanation:

Link:

Question (25)

In a circle, two chords are at distances 3 cm and 5 cm from the centre. Which chord is longer?

Explanation:

Link:

Question (26)

A chord subtends an angle of 150° at the centre. The angle subtended at the circumference in the same segment is:

Explanation:

Link:

Question (27)

In a circle, if two chords are equidistant from the centre, then they are:

Explanation:

Link:

Question (28)

A circle has radius 17 cm. A chord is 8 cm from the centre. The length of the chord is:

Explanation:

Link:

Question (29)

If a chord subtends equal angles at two different points on the same segment of a circle, then the points and endpoints of the chord form:

Explanation:

Link:

Question (30)

A wheel has spokes connected to two points on its rim by a tight string. When the wheel rotates, the angle subtended by the string at the centre:

Explanation:

Link:

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