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Question (31)

QN009488

A chord is drawn in a circle such that the line from the centre to the chord forms a right angle at its midpoint. This shows that the line from the centre is a:

(A) Tangent
(B) Perpendicular bisector
(C) Diameter only
(D) Secant

Correct Answer: B

Explanation:

The line from the centre is the perpendicular bisector of the chord.

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Question (32)

QN009489

A circle has radius 26 cm and a chord is 10 cm from the centre. The chord length is:

(A) 24 cm
(B) 36 cm
(C) 48 cm
(D) 52 cm

Correct Answer: C

Explanation:

Half chord = √(26²−10²)=24 cm, so chord = 48 cm.

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Question (33)

QN009490

If a chord moves away from the centre of a circle while remaining parallel to itself, then its length:

(A) Increases
(B) Remains same
(C) Decreases
(D) Doubles

Correct Answer: C

Explanation:

Chords farther from the centre become shorter.

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Question (34)

QN009491

In a circle of radius 25 cm, the distance from the centre to a chord is 24 cm. The chord length is:

(A) 7 cm
(B) 12 cm
(C) 14 cm
(D) 48 cm

Correct Answer: C

Explanation:

Half chord = √(25²−24²)=7 cm, so chord = 14 cm.

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Question (35)

QN009492

The line segment joining the centre to the midpoint of a chord creates which type of triangle with the chord endpoints?

(A) Scalene triangle
(B) Equilateral triangle
(C) Two congruent right triangles
(D) Obtuse triangle

Correct Answer: C

Explanation:

The perpendicular from the centre divides the triangle into two congruent right triangles.

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Question (36)

QN009493

Two parallel chords of lengths 6 cm and 8 cm lie on opposite sides of the centre of a circle of radius 5 cm. The distance between the midpoints of the chords is:

(A) 2 cm
(B) 4 cm
(C) 6 cm
(D) 8 cm

Correct Answer: C

Explanation:

Distances from centre are 4 cm and 3 cm. Total distance = 4 + 2 = 6 cm.

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Question (37)

QN009494

A chord of length 40 cm is at a distance of 9 cm from the centre. The radius is:

(A) 21 cm
(B) 29 cm
(C) 31 cm
(D) 41 cm

Correct Answer: A

Explanation:

Half chord = 20 cm. Radius = √(20²+9²)=21 cm.

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Question (38)

QN009495

The converse of “the line joining the centre and midpoint of a chord is perpendicular to the chord” is:

(A) Equal chords subtend equal angles
(B) Perpendicular from centre bisects the chord
(C) Diameter is the longest chord
(D) Radius is half the diameter

Correct Answer: B

Explanation:

A perpendicular from the centre to a chord bisects the chord.

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Question (39)

QN009496

In a circle, a chord of length 8 cm is at a distance of 15 cm from the centre. The radius is:

(A) 15 cm
(B) 16 cm
(C) 17 cm
(D) 19 cm

Correct Answer: C

Explanation:

Half chord = 4 cm. Radius = √(15²+4²)=17 cm.

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Question (40)

QN009497

The midpoint of a chord and the centre of the circle are joined. If the radius is 13 cm and half the chord is 5 cm, then the distance from the centre to the chord is:

(A) 5 cm
(B) 8 cm
(C) 12 cm
(D) 13 cm

Correct Answer: C

Explanation:

Distance = √(13²−5²)=12 cm.

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Question (31)

A chord is drawn in a circle such that the line from the centre to the chord forms a right angle at its midpoint. This shows that the line from the centre is a:

Explanation:

Link:

Question (32)

A circle has radius 26 cm and a chord is 10 cm from the centre. The chord length is:

Explanation:

Link:

Question (33)

If a chord moves away from the centre of a circle while remaining parallel to itself, then its length:

Explanation:

Link:

Question (34)

In a circle of radius 25 cm, the distance from the centre to a chord is 24 cm. The chord length is:

Explanation:

Link:

Question (35)

The line segment joining the centre to the midpoint of a chord creates which type of triangle with the chord endpoints?

Explanation:

Link:

Question (36)

Two parallel chords of lengths 6 cm and 8 cm lie on opposite sides of the centre of a circle of radius 5 cm. The distance between the midpoints of the chords is:

Explanation:

Link:

Question (37)

A chord of length 40 cm is at a distance of 9 cm from the centre. The radius is:

Explanation:

Link:

Question (38)

The converse of “the line joining the centre and midpoint of a chord is perpendicular to the chord” is:

Explanation:

Link:

Question (39)

In a circle, a chord of length 8 cm is at a distance of 15 cm from the centre. The radius is:

Explanation:

Link:

Question (40)

The midpoint of a chord and the centre of the circle are joined. If the radius is 13 cm and half the chord is 5 cm, then the distance from the centre to the chord is:

Explanation:

Link:

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