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Question (11)

QN009468

A chord of length 16 cm is at a distance of 6 cm from the centre of a circle. The radius is:

(A) 8 cm
(B) 9 cm
(C) 10 cm
(D) 12 cm

Correct Answer: C

Explanation:

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

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Question (12)

QN009469

Which chord is nearest to the centre of a circle?

(A) Smallest chord
(B) Diameter
(C) Chord of length 1 cm
(D) Any random chord

Correct Answer: B

Explanation:

Diameter passes through the centre, so distance is zero.

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Question (13)

QN009470

In a circle, longer chords are:

(A) Farther from the centre
(B) Closer to the centre
(C) Equal in distance from the centre
(D) Tangential to the circle

Correct Answer: B

Explanation:

Longer chords lie nearer to the centre.

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Question (14)

QN009471

A chord of length 18 cm lies 12 cm away from the centre. The radius of the circle is:

(A) 12 cm
(B) 13 cm
(C) 15 cm
(D) 18 cm

Correct Answer: C

Explanation:

Half chord = 9 cm. Radius = √(12²+9²)=15 cm.

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Question (15)

QN009472

The perpendicular bisector of a chord always passes through the:

(A) Tangent point
(B) Arc midpoint
(C) Centre of the circle
(D) Radius midpoint

Correct Answer: C

Explanation:

The perpendicular bisector of a chord passes through the centre.

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Question (16)

QN009473

A chord of a circle has length 14 cm. If the radius is 25 cm, the distance of the chord from the centre is:

(A) 7 cm
(B) 24 cm
(C) 20 cm
(D) 18 cm

Correct Answer: B

Explanation:

Half chord = 7 cm. Distance = √(25²−7²)=24 cm.

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Question (17)

QN009474

If two chords are unequal, then the longer chord lies:

(A) Closer to the centre
(B) Farther from the centre
(C) At the same distance from the centre
(D) On the diameter

Correct Answer: A

Explanation:

Longer chords lie closer to the centre.

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Question (18)

QN009475

In a circle, a perpendicular drawn from the centre to a chord divides the chord into segments of 9 cm each. The full chord length is:

(A) 9 cm
(B) 12 cm
(C) 18 cm
(D) 36 cm

Correct Answer: C

Explanation:

Full chord length = 2 × 9 = 18 cm.

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Question (19)

QN009476

A circle has radius 10 cm. A chord is 8 cm from the centre. The chord length is:

(A) 6 cm
(B) 8 cm
(C) 12 cm
(D) 16 cm

Correct Answer: C

Explanation:

Half chord = √(10²−8²)=6 cm, so chord = 12 cm.

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Question (20)

QN009477

Which theorem is used to prove that equal chords are equidistant from the centre?

(A) Midpoint theorem
(B) Pythagoras theorem
(C) Exterior angle theorem
(D) Basic proportionality theorem

Correct Answer: B

Explanation:

Pythagoras theorem is used in the proof.

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Question (11)

A chord of length 16 cm is at a distance of 6 cm from the centre of a circle. The radius is:

Explanation:

Link:

Question (12)

Which chord is nearest to the centre of a circle?

Explanation:

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Question (13)

In a circle, longer chords are:

Explanation:

Link:

Question (14)

A chord of length 18 cm lies 12 cm away from the centre. The radius of the circle is:

Explanation:

Link:

Question (15)

The perpendicular bisector of a chord always passes through the:

Explanation:

Link:

Question (16)

A chord of a circle has length 14 cm. If the radius is 25 cm, the distance of the chord from the centre is:

Explanation:

Link:

Question (17)

If two chords are unequal, then the longer chord lies:

Explanation:

Link:

Question (18)

In a circle, a perpendicular drawn from the centre to a chord divides the chord into segments of 9 cm each. The full chord length is:

Explanation:

Link:

Question (19)

A circle has radius 10 cm. A chord is 8 cm from the centre. The chord length is:

Explanation:

Link:

Question (20)

Which theorem is used to prove that equal chords are equidistant from the centre?

Explanation:

Link:

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