Class 9 Maths – Circles MCQ

1. The radius of a circle is:

a) The longest chord
b) Half the diameter
c) Tangent to the circle
d) A line joining the center to any point on the circle

Answer:

d) A line joining the center to any point on the circle

Explanation:

Radius is a segment whose endpoints are the center and a point on the circle.

2. A chord of a circle that passes through the center is called:

a) A diameter
b) A radius
c) A segment
d) A sector

Answer:

a) A diameter

Explanation:

A diameter is a special chord that passes through the center, dividing the circle into two equal parts.

3. The number of tangents that can be drawn from an external point to a circle is:

a) One
b) Two
c) Three
d) Infinite

Answer:

b) Two

Explanation:

From an external point, two tangents can be drawn to a circle.

4. The perpendicular drawn from the center of a circle to a chord:

a) Divides the chord into two unequal parts
b) Passes through the midpoint of the chord
c) Is parallel to the chord
d) Is the longest chord of the circle

Answer:

b) Passes through the midpoint of the chord

Explanation:

The perpendicular from the center of a circle to a chord bisects the chord.

5. A circle can have ____ diameters.

a) One
b) Two
c) Three
d) Infinite

Answer:

d) Infinite

Explanation:

A circle can have infinite diameters as it can pass through the center in infinite ways.

6. The distance between the center of a circle and its chord AB is 4 cm. If the length of AB is 8 cm, then the radius of the circle is:

a) 5 cm
b) 8 cm
c) 10 cm
d) 12 cm

Answer:

a) 5 cm

Explanation:

Using the Pythagoras theorem in the right triangle formed, radius = √(AB/2)^2 + 4^2 = 5 cm.

7. A sector of a circle is the region between:

a) Two radii and the corresponding arc
b) A chord and its arc
c) Two chords
d) A tangent and its chord

Answer:

a) Two radii and the corresponding arc

Explanation:

A sector is bounded by two radii and the arc between them.

8. A line that touches the circle at exactly one point is called:

a) A chord
b) A diameter
c) A radius
d) A tangent

Answer:

d) A tangent

Explanation:

A tangent touches the circle at only one point without cutting it.

9. The common point of a tangent and the circle is called:

a) Chord
b) Segment
c) Point of contact
d) Center

Answer:

c) Point of contact

Explanation:

The point where a tangent touches the circle is called the point of contact.

10. The angle between the tangent at a point on the circle and the radius through the point is always:

a) 0°
b) 45°
c) 90°
d) 180°

Answer:

c) 90°

Explanation:

The radius at the point of contact is always perpendicular to the tangent.

11. The circle with the maximum area among all the circles with the same circumference is:

a) A semicircle
b) A sector
c) A circle itself
d) A segment

Answer:

c) A circle itself

Explanation:

Among all shapes with a given perimeter, a circle has the maximum area.

12. Equal chords of a circle subtend ____ angles at the center.

a) Acute
b) Obtuse
c) Equal
d) Right

Answer:

c) Equal

Explanation:

Equal chords of a circle subtend equal angles at the center.

13. The length of a chord of a circle is 10 cm and its distance from the center is 4 cm. The radius of the circle is:

a) 6 cm
b) 8.2 cm
c) 7 cm
d) 5 cm

Answer:

b) 8.2 cm

Explanation:

Using Pythagoras theorem in the right triangle formed, radius = √(chord/2)^2 + 4^2 = 8.2 cm.

14. The chord of a circle, which is twice as long as its radius, subtends an angle of:

a) 60°
b) 90°
c) 120°
d) 180°

Answer:

a) 60°

Explanation:

In such a case, the angle subtended by the chord at the center of the circle is 60°.

15. Two circles touching each other externally touch at:

a) One point
b) Two points
c) Three points
d) Infinite points

Answer:

a) One point

Explanation:

Two circles touching each other externally will touch at exactly one point.

16. The distance between the centers of two circles touching each other externally is:

a) Zero
b) Equal to the sum of their radii
c) Equal to the difference of their radii
d) Infinite

Answer:

b) Equal to the sum of their radii

Explanation:

The distance between their centers will be the sum of their radii.

17. In a circle of radius 14 cm, an arc subtends an angle of 60° at the center. The length of the arc is:

a) 14/3 cm
b) 14π/3 cm
c) 7π/3 cm
d) 28π/3 cm

Answer:

b) 14π/3 cm

Explanation:

Length of the arc = (60/360) × 2π × 14 = 14π/3 cm.

18. If a circle is divided into three equal arcs, each arc will subtend ____ angle at the center.

a) 60°
b) 90°
c) 120°
d) 180°

Answer:

c) 120°

Explanation:

Each arc will subtend 1/3 of 360°, which is 120°.

19. If two circles touch internally, the point of contact lies:

a) Outside both the circles
b) In between the centers of the two circles
c) On the larger circle
d) On the smaller circle

Answer:

d) On the smaller circle

Explanation:

For two circles touching internally, the point of contact lies on the circumference of the smaller circle.

20. The number of tangents that can be drawn to a circle from a point on the circle is:

a) Zero
b) One
c) Two
d) Infinite

Answer:

a) Zero

Explanation:

No tangent can be drawn from a point lying on the circle.

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