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Question (11)

QN009428

In a circle of radius 13 cm, the perpendicular distance from the centre to a chord is 5 cm. The length of the chord is:

(A) 10 cm
(B) 12 cm
(C) 24 cm
(D) 26 cm

Correct Answer: C

Explanation:

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

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Question (12)

QN009429

Two chords of lengths 12 cm and 16 cm are drawn in the same circle. Which statement is correct?

(A) The 12 cm chord is nearer to the centre
(B) Both are equidistant from the centre
(C) The 16 cm chord is nearer to the centre
(D) Cannot be determined

Correct Answer: C

Explanation:

Longer chord lies nearer to the centre.

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Question (13)

QN009430

A chord of length 14 cm is at a distance of 24 cm from the centre of a circle. The radius of the circle is:

(A) 25 cm
(B) 26 cm
(C) 27 cm
(D) 28 cm

Correct Answer: A

Explanation:

Radius = √(24²+7²)=25 cm.

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Question (14)

QN009431

If the radius of a circle is doubled, then the length of a chord at the same perpendicular distance from the centre will:

(A) Decrease
(B) Remain same
(C) Increase
(D) Become zero

Correct Answer: C

Explanation:

Larger radius gives longer chord at same distance.

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Question (15)

QN009432

In a circle, two equal chords AB and CD subtend central angles (3x+10)° and (5x−30)° respectively. The value of x is:

(A) 15
(B) 18
(C) 20
(D) 25

Correct Answer: C

Explanation:

3x+10 = 5x−30 ⇒ x = 20.

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Question (16)

QN009433

A chord subtends an angle of 110° at the centre. What angle will it subtend at a point on the major arc?

(A) 35°
(B) 45°
(C) 55°
(D) 110°

Correct Answer: C

Explanation:

Angle at circumference = 110°/2 = 55°.

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Question (17)

QN009434

The angle subtended by an arc at the centre is always ______ the angle subtended by it at any point on the remaining circle.

(A) Half
(B) Double
(C) Triple
(D) Equal to

Correct Answer: B

Explanation:

Angle at centre is double the angle at circumference.

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Question (18)

QN009435

In a circle, chord AB subtends an angle of 70° at the circumference. The angle subtended by the same chord at the centre is:

(A) 35°
(B) 70°
(C) 140°
(D) 210°

Correct Answer: C

Explanation:

Angle at centre = 2 × 70° = 140°.

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Question (19)

QN009436

A chord of a circle is equal in length to the radius of the circle. The angle subtended by the chord at the centre is:

(A) 30°
(B) 45°
(C) 60°
(D) 90°

Correct Answer: C

Explanation:

Radius-radius-chord forms an equilateral triangle.

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Question (20)

QN009437

In a circle, if a chord is moved closer to the centre while remaining parallel to its previous position, its length:

(A) Decreases
(B) Increases
(C) Remains unchanged
(D) Becomes zero

Correct Answer: B

Explanation:

Chords nearer to the centre are longer.

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Question (11)

In a circle of radius 13 cm, the perpendicular distance from the centre to a chord is 5 cm. The length of the chord is:

Explanation:

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Question (12)

Two chords of lengths 12 cm and 16 cm are drawn in the same circle. Which statement is correct?

Explanation:

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Question (13)

A chord of length 14 cm is at a distance of 24 cm from the centre of a circle. The radius of the circle is:

Explanation:

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Question (14)

If the radius of a circle is doubled, then the length of a chord at the same perpendicular distance from the centre will:

Explanation:

Link:

Question (15)

In a circle, two equal chords AB and CD subtend central angles (3x+10)° and (5x−30)° respectively. The value of x is:

Explanation:

Link:

Question (16)

A chord subtends an angle of 110° at the centre. What angle will it subtend at a point on the major arc?

Explanation:

Link:

Question (17)

The angle subtended by an arc at the centre is always ______ the angle subtended by it at any point on the remaining circle.

Explanation:

Link:

Question (18)

In a circle, chord AB subtends an angle of 70° at the circumference. The angle subtended by the same chord at the centre is:

Explanation:

Link:

Question (19)

A chord of a circle is equal in length to the radius of the circle. The angle subtended by the chord at the centre is:

Explanation:

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Question (20)

In a circle, if a chord is moved closer to the centre while remaining parallel to its previous position, its length:

Explanation:

Link:

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