Class 10 Maths Chapter 10 Circles MCQs Quiz

Are you confused by the geometric theorems and concepts about tangents in Chapter 10, ‘Circles’? Are proof-based questions from this chapter causing you anxiety for the board exam? Your worries are over! We have created the perfect resource for you: the Class 10 Maths Chapter 10 Circles MCQs Quiz. This free online test will help you clear all your concepts and understand the pattern of questions asked in the exam. Let’s strengthen your board exam preparation with this effective Circles quiz!

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Circles MCQs Quiz

Click the Start button to begin the quiz and attempt all questions within the given time. Read each MCQ carefully, select the correct option, and move forward to complete the quiz. Your score will appear at the end to help you check your preparation level..

Q1: At how many points does a tangent to a circle intersect it?

A: Zero
B: One
C: Two
D: Countless

Explanation: A tangent touches the circle at exactly one point.

Q2: What is the line that intersects a circle at two points called?

A: Tangent
B: Secant
C: Non-intersecting line
D: Normal

Explanation: A line that cuts the circle at two points is called a secant.

Q3: How is the tangent to a circle related to the radius passing through the point of contact?

A: Parallel
B: Perpendicular
C: Oblique
D: Coincident

Explanation: According to the theorem, the tangent is perpendicular to the radius.

Q4: From a point inside a circle, how many tangents can be drawn?

A: One
B: Two
C: None
D: Countless

Explanation: No tangent is possible from an interior point.

Q5: From a point outside a circle, how many tangents can be drawn?

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

Explanation: Exactly two tangents can be drawn from an external point.

Q6: How are the lengths of the two tangents drawn from an external point?

A: Unequal
B: Equal
C: Double
D: Half

Explanation: According to the theorem, the lengths of both tangents are equal.

Q7: From a point, the length of the tangent is 24 cm and the distance from the center is 25 cm. What is the radius?

A: 7 cm
B: 12 cm
C: 15 cm
D: 24.5 cm

Explanation: By Pythagoras theorem: r = √(25² – 24²) = √(625 – 576) = √49 = 7 cm.

Q8: If the radius is 5 cm and OQ = 12 cm, then what is the length of tangent PQ?

A: 12 cm
B: 13 cm
C: 8.5 cm
D: √119 cm

Explanation: PQ = √(12² – 5²) = √(144 – 25) = √119 cm.

Q9: If ∠POQ = 110°, then what is the angle between the two tangents?

A: 60°
B: 70°
C: 80°
D: 90°

Explanation: In quadrilateral OPTQ, the sum of angles is 360°.
Angles at P and Q are 90° each (tangent ⟂ radius).
So, ∠PTQ = 360° – (90° + 90° + 110°) = 70°.

Q10: If ∠APB = 80°, then what is the value of ∠POA?

A: 50°
B: 60°
C: 70°
D: 80°

Explanation: OP bisects ∠APB, so ∠APO = 40°.
In right triangle OAP, ∠POA = 90° – 40° = 50°.

Q11: The radii of two concentric circles are 5 cm and 3 cm. What is the length of the chord that is tangent to the inner circle?

A: 4 cm
B: 6 cm
C: 8 cm
D: 10 cm

Explanation: The perpendicular from the center to the chord equals the inner radius (3 cm).
Half the chord length = √(5² – 3²) = √(25-9) = √16 = 4 cm.
Full chord length = 2 × 4 = 8 cm.

Q12: Which property holds true for a quadrilateral circumscribing a circle?

A: AB + BC = CD + DA
B: AB + CD = AD + BC
C: AB + AD = BC + CD
D: AC + BD = AB + CD

Explanation: The sums of opposite sides of a circumscribed quadrilateral are equal.

Q13: What are the tangents drawn at the ends of a diameter of a circle like?

A: Perpendicular
B: Parallel
C: Oblique
D: Coincident

Explanation: Both tangents are parallel to each other.

Q14: A chord of the larger circle that is tangent to the smaller concentric circle is divided how?

A: Unequally
B: Bisected
C: Tripled
D: Halved

Explanation: The chord is bisected at the point of tangency.

Q15: The perpendicular drawn to the tangent at the point of contact passes through?

A: The circumference
B: The center
C: The external point
D: The midpoint of the chord

Explanation: The tangent is perpendicular to the radius, so the perpendicular passes through the center.

Quiz Results

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Class 10 Maths Chapter 10 Circles MCQs Quiz

Chapter 10, ‘Circles,’ primarily focuses on the relationship between a circle and a tangent to the circle. In this chapter, you will learn how many tangents can be drawn from a point to a circle and their properties. You will study the important theorem that the tangent at any point on a circle is perpendicular to the radius at that point. You will also learn the theorem that states the lengths of the two tangents drawn from an external point to a circle are equal. These concepts related to Tangents to a Circle Class 10 are very important for the CBSE Class 10 Maths Qui and board exams.

Conclusion

Mastery of a geometry chapter like ‘Circles’ comes from clearly understanding the concepts and practicing them consistently. Our Class 10 Maths Chapter 10 Circles MCQs Quiz is designed to give your practice a clear direction. This quiz helps you strengthen your grip on the Properties of Tangents and the important theorems. By solving these objective questions, you can identify your mistakes and work on them, which is extremely beneficial for your Board Exam Preparation. Take this Free Online Maths Quiz for Class 10 now and score high!

FAQs on Circles MCQs

1. Question: How many marks from the chapter Circles are asked in the board exam?
Answer: This chapter typically carries 6-7 marks in the CBSE board exam, including MCQs, short answer, and long answer (proof-based) questions.

2. Question: What is the most important theorem in this chapter?
Answer: The most important theorem is that the tangent at any point on a circle is perpendicular to the radius through the point of contact.

3. Question: Is this Circles quiz based on the NCERT syllabus?
Answer: Yes, our Circles Class 10 MCQ quiz is fully based on the NCERT curriculum and the CBSE syllabus.

4. Question: How many tangents can be drawn from a point outside a circle?
Answer: Two tangents can be drawn from a point outside a circle.

5. Question: Can a tangent be drawn from a point inside a circle?
Answer: No, a tangent cannot be drawn from a point inside a circle.

6. Question: Is this online quiz free?
Answer: Yes, this Free Online Maths Quiz for Class 10 is absolutely free. You can take it anytime and anywhere for practice.

7. Question: How should I prepare this chapter for the board exam?
Answer: First, understand all the theorems and their constructions. Then, solve the examples and exercise questions from the NCERT book. Finally, test your skills with our Circles Online Test.

8. Question: What is the relationship between the lengths of two tangents drawn from an external point?
Answer: The lengths of the two tangents drawn from an external point to a circle are equal.

9. Question: Does this quiz include proof-based questions?
Answer: This quiz is primarily MCQ-based, but it will strengthen your concepts to a level where you can easily solve proof-based questions.

10. Question: What is the benefit of taking this online quiz?
Answer: This quiz helps you improve time management, check the accuracy of your concepts, and understand the exam pattern, which boosts your confidence and leads to better performance.

Practice with our free Class 10 Maths Chapter 10 Circles MCQs Quiz. This online test covers important concepts like properties of tangents and theorems, based on the NCERT syllabus. Perfect for CBSE board exam preparation. Take the quiz now and score high!

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Circles MCQs Quiz

Quiz Results

Class 10 Maths Chapter 10 Circles MCQs Quiz

Conclusion

FAQs on Circles MCQs

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