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Question (1)

QN0026586

In a circle, a chord subtends an angle of 64° at a point on the circle. The angle subtended by the same chord at the centre is:

(A) 32°
(B) 64°
(C) 96°
(D) 128°

Correct Answer: D

Explanation:

Angle at centre = 2 × 64° = 128°.

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Question (2)

QN0026587

A chord of length 16 cm is at a distance of 12 cm from the centre of a circle. The radius of the circle is:

(A) 14 cm
(B) 15 cm
(C) 16 cm
(D) 20 cm

Correct Answer: A

Explanation:

Half chord = 8 cm. Radius = √(8² + 12²) = √208 ≈ 14 cm.

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Question (3)

QN0026588

Which of the following statements is always true?

(A) Equal chords are parallel
(B) Equal chords are equidistant from the centre
(C) Every chord is a diameter
(D) Longer chords are farther from the centre

Correct Answer: B

Explanation:

Equal chords are equidistant from the centre.

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Question (4)

QN0026589

In a cyclic quadrilateral, one angle is 78°. Its opposite angle is:

(A) 78°
(B) 92°
(C) 102°
(D) 112°

Correct Answer: C

Explanation:

Opposite angles of a cyclic quadrilateral are supplementary.

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Question (5)

QN0026590

The angle subtended by a diameter at any point on the remaining part of the circle is:

(A) 45°
(B) 60°
(C) 90°
(D) 180°

Correct Answer: C

Explanation:

Angle in a semicircle is always 90°.

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Question (6)

QN0026591

In the same circle, which chord is longer?

(A) Chord at distance 4 cm from centre
(B) Chord at distance 7 cm from centre
(C) Both are equal
(D) Cannot be determined

Correct Answer: A

Explanation:

Chords nearer to the centre are longer.

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Question (7)

QN0026592

A chord subtends an angle of 140° at the centre. The angle subtended by the same chord at the circumference is:

(A) 40°
(B) 60°
(C) 70°
(D) 140°

Correct Answer: C

Explanation:

Angle at circumference = 140° ÷ 2 = 70°.

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Question (8)

QN0026593

Four points lying on the same circle are called:

(A) Concurrent points
(B) Collinear points
(C) Concyclic points
(D) Coplanar points

Correct Answer: C

Explanation:

Points lying on the same circle are called concyclic points.

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Question (9)

QN0026594

A circle has radius 13 cm. A chord is at a distance of 5 cm from the centre. The length of the chord is:

(A) 12 cm
(B) 20 cm
(C) 24 cm
(D) 26 cm

Correct Answer: C

Explanation:

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

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Question (10)

QN0026595

Which quadrilateral is always cyclic?

(A) Rectangle
(B) Rhombus
(C) Parallelogram
(D) Kite

Correct Answer: A

Explanation:

Every rectangle is a cyclic quadrilateral.

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Question (1)

In a circle, a chord subtends an angle of 64° at a point on the circle. The angle subtended by the same chord at the centre is:

Explanation:

Link:

Question (2)

A chord of length 16 cm is at a distance of 12 cm from the centre of a circle. The radius of the circle is:

Explanation:

Link:

Question (3)

Which of the following statements is always true?

Explanation:

Link:

Question (4)

In a cyclic quadrilateral, one angle is 78°. Its opposite angle is:

Explanation:

Link:

Question (5)

The angle subtended by a diameter at any point on the remaining part of the circle is:

Explanation:

Link:

Question (6)

In the same circle, which chord is longer?

Explanation:

Link:

Question (7)

A chord subtends an angle of 140° at the centre. The angle subtended by the same chord at the circumference is:

Explanation:

Link:

Question (8)

Four points lying on the same circle are called:

Explanation:

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Question (9)

A circle has radius 13 cm. A chord is at a distance of 5 cm from the centre. The length of the chord is:

Explanation:

Link:

Question (10)

Which quadrilateral is always cyclic?

Explanation:

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