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Question (31)

QN009448

In a circle, a chord of length 20 cm is at a distance of 24 cm from the centre. The radius is:

(A) 25 cm
(B) 26 cm
(C) 28 cm
(D) 30 cm

Correct Answer: B

Explanation:

Half chord = 10 cm. Radius = √(24² + 10²) = √676 = 26 cm.

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Question (32)

QN009449

Which statement is correct regarding equal chords in the same circle?

(A) They subtend supplementary angles at the centre
(B) They are at unequal distances from the centre
(C) They subtend equal angles at the centre
(D) They are always diameters

Correct Answer: C

Explanation:

Equal chords subtend equal angles at the centre.

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Question (33)

QN009450

A chord subtends a right angle at the centre. The angle subtended by the same chord at a point on the circle is:

(A) 30°
(B) 45°
(C) 60°
(D) 90°

Correct Answer: B

Explanation:

Angle at circumference = half of angle at centre = 45°.

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Question (34)

QN009451

In a circle, chord AB subtends angle x° at the centre and 40° at a point on the remaining circle. The value of x is:

(A) 20°
(B) 40°
(C) 80°
(D) 160°

Correct Answer: C

Explanation:

Angle at centre = 2 × angle at circumference = 80°.

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Question (35)

QN009452

A chord of a circle is perpendicular to the radius through its midpoint. This property helps mainly in:

(A) Measuring area
(B) Locating centre
(C) Finding tangent length
(D) Drawing polygons

Correct Answer: B

Explanation:

This property is used to locate the centre of the circle.

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Question (36)

QN009453

Two equal chords subtend angles (2x+15)° and (5x−60)° at the centre. Find x.

(A) 20
(B) 22
(C) 25
(D) 30

Correct Answer: C

Explanation:

2x+15 = 5x−60 ⇒ 3x = 75 ⇒ x = 25.

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Question (37)

QN009454

A student claims that every chord passing nearer to the centre becomes shorter. The statement is:

(A) True
(B) False
(C) True only for diameters
(D) True only for equal chords

Correct Answer: B

Explanation:

Chords nearer to the centre are longer, not shorter.

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Question (38)

QN009455

In a circle, the radius is 25 cm and the chord length is 48 cm. The perpendicular distance from the centre to the chord is:

(A) 5 cm
(B) 7 cm
(C) 9 cm
(D) 11 cm

Correct Answer: B

Explanation:

Half chord = 24 cm. Distance = √(25²−24²) = √49 = 7 cm.

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Question (39)

QN009456

A chord divides the circle into two arcs. The smaller arc is called the:

(A) Major arc
(B) Minor arc
(C) Reflex arc
(D) Diameter arc

Correct Answer: B

Explanation:

The smaller arc formed by a chord is called the minor arc.

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Question (40)

QN009457

If a chord subtends 90° at the circumference, then the angle subtended by the same chord at the centre is:

(A) 45°
(B) 90°
(C) 135°
(D) 180°

Correct Answer: D

Explanation:

Angle at centre = 2 × 90° = 180°.

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Question (31)

In a circle, a chord of length 20 cm is at a distance of 24 cm from the centre. The radius is:

Explanation:

Link:

Question (32)

Which statement is correct regarding equal chords in the same circle?

Explanation:

Link:

Question (33)

A chord subtends a right angle at the centre. The angle subtended by the same chord at a point on the circle is:

Explanation:

Link:

Question (34)

In a circle, chord AB subtends angle x° at the centre and 40° at a point on the remaining circle. The value of x is:

Explanation:

Link:

Question (35)

A chord of a circle is perpendicular to the radius through its midpoint. This property helps mainly in:

Explanation:

Link:

Question (36)

Two equal chords subtend angles (2x+15)° and (5x−60)° at the centre. Find x.

Explanation:

Link:

Question (37)

A student claims that every chord passing nearer to the centre becomes shorter. The statement is:

Explanation:

Link:

Question (38)

In a circle, the radius is 25 cm and the chord length is 48 cm. The perpendicular distance from the centre to the chord is:

Explanation:

Link:

Question (39)

A chord divides the circle into two arcs. The smaller arc is called the:

Explanation:

Link:

Question (40)

If a chord subtends 90° at the circumference, then the angle subtended by the same chord at the centre is:

Explanation:

Link:

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