Grade 10 Maths: Circles Interactive Quiz | Concept of Maths

Question 1

1. A tangent to a circle intersects the circle in exactly how many points?

A) 1

B) 2

C) 3

D) Infinite

Answer

Correct Answer: A

Question 2

2. A line intersecting a circle in two distinct points is called a:

A) Tangent

B) Secant

C) Chord

D) Diameter

Answer

Correct Answer: B

Question 3

3. At most, how many parallel tangents can a circle have simultaneously?

A) 1

B) Infinite

C) 2

D) 4

Answer

Correct Answer: C

Question 4

4. The common point of a tangent to a circle and the circle itself is called the:

A) Point of contact

B) Center

C) Point of intersection

D) Exterior point

Answer

Correct Answer: A

Question 5

5. The length of a tangent from a point A at distance \( 5 \text{ cm} \) from the centre of the circle is \( 4 \text{ cm} \). What is the radius of the circle?

Question 6

6. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of \( 80^\circ \), then \( \angle POA \) is equal to:

A) \( 50^\circ \)

B) \( 60^\circ \)

C) \( 70^\circ \)

D) \( 80^\circ \)

Answer

Correct Answer: A

Question 7

7. From a point Q, the length of the tangent to a circle is \( 24 \text{ cm} \) and the distance of Q from the centre is \( 25 \text{ cm} \). The radius of the circle is:

A) \( 7 \text{ cm} \)

B) \( 12 \text{ cm} \)

C) \( 15 \text{ cm} \)

D) \( 24.5 \text{ cm} \)

Answer

Correct Answer: A

Question 8

8. Two concentric circles are of radii \( 5 \text{ cm} \) and \( 3 \text{ cm} \). Find the length of the chord of the larger circle which touches the smaller circle.

A) \( 4 \text{ cm} \)

B) \( 5 \text{ cm} \)

C) \( 8 \text{ cm} \)

D) \( 10 \text{ cm} \)

Answer

Correct Answer: C

Question 9

9. A quadrilateral ABCD is drawn to circumscribe a circle. Which of the following relations is always true?

A) \( AB + BC = CD + AD \)

B) \( AB \times CD = BC \times AD \)

C) \( AB + AD = BC + CD \)

D) \( AB + CD = AD + BC \)

Answer

Correct Answer: D

Question 10

10. In a circle of radius \( 5 \text{ cm} \), a tangent at a point P intersects a line through the centre O at point Q so that \( OQ = 12 \text{ cm} \). Length PQ is:

A) \( 12 \text{ cm} \)

B) \( \sqrt{119} \text{ cm} \)

C) \( 13 \text{ cm} \)

D) \( 8.5 \text{ cm} \)

Answer

Correct Answer: B

Question 11

11. The number of tangents that can be drawn to a circle from a point situated strictly inside the circle is:

A) 2

B) 1

C) Infinite

D) 0

Answer

Correct Answer: D

Question 12

12. If two tangents inclined at an angle of \( 60^\circ \) are drawn to a circle of radius \( 3 \text{ cm} \), then the length of each tangent is equal to:

A) \( \frac{3\sqrt{3}}{2} \text{ cm} \)

B) \( 3 \text{ cm} \)

C) \( 3\sqrt{3} \text{ cm} \)

D) \( 6 \text{ cm} \)

Answer

Correct Answer: C

Question 13

13. PT is a tangent at point T to a circle whose centre is O. If \( OP = 17 \text{ cm} \) and \( OT = 8 \text{ cm} \), find the length of tangent PT.

A) \( 15 \text{ cm} \)

B) \( 25 \text{ cm} \)

C) \( 9 \text{ cm} \)

D) \( 12 \text{ cm} \)

Answer

Correct Answer: A

Question 14

14. The radii of two concentric circles are \( 4 \text{ cm} \) and \( 5 \text{ cm} \). Find the length of the chord of the larger circle which is tangent to the smaller circle.

A) \( 3 \text{ cm} \)

B) \( 6 \text{ cm} \)

C) \( 8 \text{ cm} \)

D) \( 9 \text{ cm} \)

Answer

Correct Answer: B

Question 15

15. If the angle between two radii of a circle is \( 130^\circ \), then the angle between the tangents drawn at the ends of these radii is:

A) \( 90^\circ \)

B) \( 50^\circ \)

C) \( 40^\circ \)

D) \( 70^\circ \)

Answer

Correct Answer: B

Question 16

16. According to a key circle theorem, the lengths of two tangents drawn from an external point to a circle are:

A) Perpendicular to each other

B) Always in the ratio 2:1

C) Equal

D) Unequal

Answer

Correct Answer: C

Question 17

17. At one end A of a diameter AB of a circle of radius \( 5 \text{ cm} \), tangent XAY is drawn. The length of the chord CD parallel to XY and at a distance of \( 8 \text{ cm} \) from A is:

A) \( 8 \text{ cm} \)

B) \( 6 \text{ cm} \)

C) \( 5 \text{ cm} \)

D) \( 4 \text{ cm} \)

Answer

Correct Answer: A

Question 18

18. A point P is \( 13 \text{ cm} \) from the centre of the circle. The length of the tangent drawn from P to the circle is \( 12 \text{ cm} \). What is the radius of the circle?

A) \( 7 \text{ cm} \)

B) \( 5 \text{ cm} \)

C) \( 8 \text{ cm} \)

D) \( 10 \text{ cm} \)

Answer

Correct Answer: B

Question 19

19. Two parallel lines touch the circle at points A and B respectively. If the area of the circle is \( 25\pi \text{ cm}^2 \), then the length of AB is equal to:

A) \( 5 \text{ cm} \)

B) \( 8 \text{ cm} \)

C) \( 12 \text{ cm} \)

D) \( 10 \text{ cm} \)

Answer

Correct Answer: D

Question 20

20. What is the angle subtended by a tangent to a circle at its point of contact with the corresponding radius?

A) \( 90^\circ \)

B) \( 180^\circ \)

C) \( 45^\circ \)

D) \( 60^\circ \)

Answer

Correct Answer: A

Accepted Answer

Correct Answer: B

Mastering Circles: Grade 10 Mathematics Interactive Quiz | Concept of Maths

Mastering Circles: Grade 10 Mathematics Interactive Quiz | Concept of Maths

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6. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of \( 80^\circ \), then \( \angle POA \) is equal to:

7. From a point Q, the length of the tangent to a circle is \( 24 \text{ cm} \) and the distance of Q from the centre is \( 25 \text{ cm} \). The radius of the circle is:

8. Two concentric circles are of radii \( 5 \text{ cm} \) and \( 3 \text{ cm} \). Find the length of the chord of the larger circle which touches the smaller circle.

9. A quadrilateral ABCD is drawn to circumscribe a circle. Which of the following relations is always true?

10. In a circle of radius \( 5 \text{ cm} \), a tangent at a point P intersects a line through the centre O at point Q so that \( OQ = 12 \text{ cm} \). Length PQ is:

11. The number of tangents that can be drawn to a circle from a point situated strictly inside the circle is:

12. If two tangents inclined at an angle of \( 60^\circ \) are drawn to a circle of radius \( 3 \text{ cm} \), then the length of each tangent is equal to:

13. PT is a tangent at point T to a circle whose centre is O. If \( OP = 17 \text{ cm} \) and \( OT = 8 \text{ cm} \), find the length of tangent PT.

14. The radii of two concentric circles are \( 4 \text{ cm} \) and \( 5 \text{ cm} \). Find the length of the chord of the larger circle which is tangent to the smaller circle.

15. If the angle between two radii of a circle is \( 130^\circ \), then the angle between the tangents drawn at the ends of these radii is:

16. According to a key circle theorem, the lengths of two tangents drawn from an external point to a circle are:

17. At one end A of a diameter AB of a circle of radius \( 5 \text{ cm} \), tangent XAY is drawn. The length of the chord CD parallel to XY and at a distance of \( 8 \text{ cm} \) from A is:

18. A point P is \( 13 \text{ cm} \) from the centre of the circle. The length of the tangent drawn from P to the circle is \( 12 \text{ cm} \). What is the radius of the circle?

19. Two parallel lines touch the circle at points A and B respectively. If the area of the circle is \( 25\pi \text{ cm}^2 \), then the length of AB is equal to:

20. What is the angle subtended by a tangent to a circle at its point of contact with the corresponding radius?

Grade 10 Maths: Circles Interactive Quiz | Concept of Maths

1. A tangent to a circle intersects the circle in exactly how many points?

2. A line intersecting a circle in two distinct points is called a:

3. At most, how many parallel tangents can a circle have simultaneously?

4. The common point of a tangent to a circle and the circle itself is called the:

5. The length of a tangent from a point A at distance \( 5 \text{ cm} \) from the centre of the circle is \( 4 \text{ cm} \). What is the radius of the circle?

Mastering Circles: Grade 10 Mathematics Interactive Quiz | Concept of Maths

Mastering Circles: Grade 10 Mathematics Interactive Quiz | Concept of Maths

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6. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of \( 80^\circ \), then \( \angle POA \) is equal to:

7. From a point Q, the length of the tangent to a circle is \( 24 \text{ cm} \) and the distance of Q from the centre is \( 25 \text{ cm} \). The radius of the circle is:

8. Two concentric circles are of radii \( 5 \text{ cm} \) and \( 3 \text{ cm} \). Find the length of the chord of the larger circle which touches the smaller circle.

9. A quadrilateral ABCD is drawn to circumscribe a circle. Which of the following relations is always true?

10. In a circle of radius \( 5 \text{ cm} \), a tangent at a point P intersects a line through the centre O at point Q so that \( OQ = 12 \text{ cm} \). Length PQ is:

11. The number of tangents that can be drawn to a circle from a point situated strictly inside the circle is:

12. If two tangents inclined at an angle of \( 60^\circ \) are drawn to a circle of radius \( 3 \text{ cm} \), then the length of each tangent is equal to:

13. PT is a tangent at point T to a circle whose centre is O. If \( OP = 17 \text{ cm} \) and \( OT = 8 \text{ cm} \), find the length of tangent PT.

14. The radii of two concentric circles are \( 4 \text{ cm} \) and \( 5 \text{ cm} \). Find the length of the chord of the larger circle which is tangent to the smaller circle.

15. If the angle between two radii of a circle is \( 130^\circ \), then the angle between the tangents drawn at the ends of these radii is:

16. According to a key circle theorem, the lengths of two tangents drawn from an external point to a circle are:

17. At one end A of a diameter AB of a circle of radius \( 5 \text{ cm} \), tangent XAY is drawn. The length of the chord CD parallel to XY and at a distance of \( 8 \text{ cm} \) from A is:

18. A point P is \( 13 \text{ cm} \) from the centre of the circle. The length of the tangent drawn from P to the circle is \( 12 \text{ cm} \). What is the radius of the circle?

19. Two parallel lines touch the circle at points A and B respectively. If the area of the circle is \( 25\pi \text{ cm}^2 \), then the length of AB is equal to:

20. What is the angle subtended by a tangent to a circle at its point of contact with the corresponding radius?