30 MCQs on Circles | Class 10 Mathematics Chapter 10

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Welcome to MCQ Assam School. This post contains 30 MCQs (Multiple Choice Questions) on Class 10 Mathematics Chapter 10. The name of the chapter is “Circles”. So, basically, this post contains 30 MCQs on Circles. These MCQs will help you to understand the chapter better and will also help you prepare for your exam.

Chapter 10 of class 10 Mathematics as per the NCERT syllabus is Circles which deals with the introduction to circles, , .

MCQ on Circles Class 10 Maths Chapter 10

The Chapter deals with the following topics:

Introduction to Circles
The Tangent of a Circle and
Other Theorems Related to Circles, etc.

These MCQs can also act as a Mock Test. There are 30 MCQs. There are four options for each question. Out of the four options, only one option is correct. Choose the correct options for each question and click on the submit button to see the results. You can also, review your answers. For each right option, you will see a green check mark and for each wrong option, you will see a red cross mark. If the chosen option is wrong then a green check mark will appear near the right option. This way you will know the right answer.

Let’s begin.

MCQ on Circles | Class 10 Maths Chapter 10

1. What is a tangent to a circle?

A. A line that intersects the circle at two points B. A line that intersects the circle at one point C. A line that does not intersect the circle D. A line that is outside the circle

2. What is the point of contact in a tangent?

A. The center of the circle B. The point where the tangent touches the circle C. The radius of the circle D. The circumference of the circle

3. How many tangents can be drawn from an external point to a circle?

A. One B. Two C. None D. Three

4. If a line intersects a circle at exactly two points, what is it called?

A. Tangent B. Diameter C. Secant D. Radius

5. What is the theorem that states the tangent at any point of a circle is perpendicular to the radius through the point of contact?

A. Pythagoras Theorem B. Secant-Tangent Theorem C. Intersecting Chord Theorem D. Tangent-Radius Theorem

6. According to Theorem 10.2, what is true about the lengths of tangents drawn from an external point to a circle?

A. They are different B. They are equal C. They are perpendicular D. They are parallel

7. What does the word ‘tangent’ mean in Latin?

A. To intersect B. To touch C. To draw D. To measure

8. What is the maximum number of tangents that can be drawn to a circle parallel to a given secant?

A. One B. Two C. None D. Three

9. What happens when a line touches a circle at exactly one point?

A. It is a tangent B. It is a secant C. It is a chord D. It is a diameter

10. What is the relationship between a radius and a tangent at the point of contact?

A. They are parallel B. They are perpendicular C. They are equal D. They are opposite

11. How many common tangents can two non-intersecting circles have?

A. Four B. Three C. Two D. One

12. What is the distance from the center of a circle to a point outside the circle called?

A. Radius B. Diameter C. Length of the tangent D. Secant length

13. What is the length of the tangent from an external point to the circle if the radius is 5 cm and the distance from the center to the point is 12 cm?

A. 5 cm B. 12 cm C. 13 cm D. 8.5 cm

14. How many tangents can be drawn to a circle from a point inside the circle?

A. None B. One C. Two D. Three

15. Which theorem states that if two tangents are drawn to a circle from an external point, then they subtend equal angles at the center?

A. Alternate Segment Theorem B. Tangent-Secant Theorem C. Tangent-Tangent Theorem D. Perpendicular Tangent Theorem

16. What do you call the line segment that joins two points on the circle?

A. Tangent B. Chord C. Secant D. Radius

17. What is the measure of an angle formed by two radii of a circle?

A. 90 degrees B. 180 degrees C. Central angle D. Right angle

18. In a right-angled triangle, the hypotenuse is the side opposite to which angle?

A. Right angle B. Acute angle C. Obtuse angle D. Complementary angle

19. What is the relationship between two tangents drawn from an external point to a circle?

A. They are parallel B. They are equal in length C. They are perpendicular D. They are opposite

20. What is the formula for the length of a tangent from an external point to a circle?

A. \( \sqrt{r^2 + d^2} \) B. \( \sqrt{d^2 – r^2} \) C. \( r + d \) D. \( \sqrt{d^2 + r^2} \)

21. If the radius of a circle is 4 cm and the length of a tangent from a point outside the circle is 3 cm, what is the distance from the center to the point?

A. 3 cm B. 5 cm C. 7 cm D. 6 cm

22. Which theorem states that the angle between the tangent and the chord through the point of contact is equal to the angle in the alternate segment?

A. Tangent-Secant Theorem B. Alternate Segment Theorem C. Tangent-Tangent Theorem D. Perpendicular Tangent Theorem

23. How many points of intersection can two circles have?

A. One B. Four C. Two D. Three

24. If two circles intersect at two points, how many common tangents can they have?

A. One B. Two C. Three D. Four

25. What is the radius of a circle if the length of the tangent from a point 15 cm from the center is 9 cm?

A. 12 cm B. 12 cm C. 8 cm D. 6 cm

26. What do you call the segment that joins two points on a circle and passes through the center?

A. Chord B. Diameter C. Secant D. Tangent

27. What is the relationship between the radius and the tangent at the point of contact?

A. Parallel B. Intersecting C. Perpendicular D. Equal

28. What is a secant to a circle?

A. A line that touches the circle at one point B. A line that does not touch the circle C. A line that intersects the circle at two points D. A line that intersects the circle at three points

29. What is the measure of an angle inscribed in a semicircle?

A. 90 degrees B. 180 degrees C. 45 degrees D. 60 degrees

30. What is the distance between the centers of two circles if they are externally tangent?

A. The sum of their radii B. The difference of their radii C. The product of their radii D. The quotient of their radii

Review Your Answers Above.

MCQ on Real Numbers | Class 10 Mathematics Chapter 1
MCQ on Polynomials | Class 10 Mathematics Chapter 2
MCQ on Pair of Linear Equations in Two Variables | Class 10 Mathematics Chapter 3
MCQ on Quadratic Equations | Class 10 Mathematics Chapter 4
MCQ on Arithmetic Progressions | Class 10 Mathematics Chapter 5
MCQ on Triangles | Class 10 Mathematics Chapter 6
MCQ on Coordinate Geometry | Class 10 Mathematics Chapter 7
MCQ on Introduction to Trigonometry | Class 10 Mathematics Chapter 8
MCQ on Some Applications of Trigonometry | Class 10 Mathematics Chapter 9
MCQ on Areas Related to Circles | Class 10 Mathematics Chapter 11
MCQs on Surface Areas and Volumes | Class 10 Mathematics Chapter 12
MCQ on Statistics | Class 10 Mathematics Chapter 13
MCQ on Probability | Class 10 Mathematics Chapter 14

The Bottom Line

I hope these 30 Multiple-choice questions have helped you learn more about the Class 10 Mathematics Chapter 10 (Circles) in detail. You can retake the test anytime you want by refreshing the page and review your results.

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Abdur Rohman

Abdur Rohman is an Electrical Engineer from Charaideo, Assam, who wears multiple hats as a part-time teacher, blogger, entrepreneur, and digital marketer. Passionate about education, he founded The Assam School blog to provide free, comprehensive textbook solutions, MCQs (Multiple Choice Questions), and other academic content for students from Class V to XII.

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MCQ on Circles | Class 10 Mathematics Chapter 10