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Class 10 Maths Chapter 8 Circles Exercise 8.1 NCERT Solutions

Exercise 8.1 of Class 10 Maths Chapter 8 explains the basic concept of tangents to a circle. It focuses on the key property that a tangent is perpendicular to the radius at the point of contact. These NCERT solutions will help you understand concepts clearly and solve problems with confidence.

 

NCERT Class 10 Maths Chapter 8 Circles, introduces important concepts related to tangents and their properties. Exercise 8.1 focuses on understanding the fundamental idea of a tangent to a circle and how it behaves with respect to the radius.

This concept is a core part of the Class 10 Maths syllabus and forms the base for many geometry problems. 

In this exercise, you will learn that a tangent at any point on a circle is always perpendicular to the radius at the point of contact. These NCERT Solutions for Exercise 8.1 provide clear, step-by-step explanations that will help you through each problem.

NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.1

1. How many tangents can a circle have?

Answer:

A circle can have infinitely many tangents since there are infinitely many points on the circumference of the circle and at each point of it, it has a unique tangent.

2. Fill in the blanks: 

(i) A tangent to a circle intersects it in _______________ point(s). 

(ii) A line intersecting a circle in two points is called a _______________. 

(iii) A circle can have _______________ parallel tangents at the most. 

(iv) The common point of a tangent to a circle and the circle is called _______________.

Answer:

(i) one 

(ii) secant 

(iii) two 

(iv) point of contact 

3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. 

Length PQ is:  (A) 12 cm (B) 13 cm (C) 8.5 cm (D) √119 cm

Answer:

(D)chapter 10-Circles Exercise 10.1/image002.png
We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
∴OP ⊥ PQ By applying Pythagoras theorem in ΔOPQ,NCERT solutions for class 10 maths chapter 10-Circles Exercise 10.1/image003.png

4. Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

Answer:

chapter 10-Circles Exercise 10.1

AB || CD || EF AB, CD and EF are three parallel lines where EF is the tangent to the circle. Here CD is secant (Intersecting circle at 2 points P and Q)

How to Score Better in Class 10 Maths Exam?

Scoring well in Class 10 Maths requires clear concepts, regular practice, and a focus on accuracy and answer presentation. To score better, you should:

  • Build Strong Concepts:

Focus on understanding concepts in Class 10 Maths instead of memorising steps, as this helps in solving application-based questions.

  • Work on Weak Areas:

Focus on difficult topics from the Class 10 Maths syllabus instead of skipping them to avoid losing marks.

  • Revise Formulas Daily:

Regular revision of PW Class 10 Maths MIQs helps avoid calculation mistakes in exams.

  • Practise Regularly:

Solve all  CBSE Class 10 NCERT questions multiple times to strengthen your basics and improve accuracy.

  • Solve Previous Year Papers:

Practising  CBSE Class 10 Previous Year Question Papers (PYQs) helps you understand question patterns and important topics.

 

Introduction to Trigonometry Class 10 Maths Chapter 8 Exercise 8.1 FAQs

What topics are covered in Exercise 8.1 of Chapter 8?

Exercise 8.1 focuses on the concept of tangents to a circle, the properties of tangents, the relationship between the radius and tangent, and the length of tangents drawn from an external point.

Why is Exercise 8.1 important for students?

This exercise is crucial as it builds a strong foundation in geometry, especially in understanding tangents and circles, which are frequently asked in board exams.

Are the NCERT Solutions for Exercise 8.1 sufficient for board exam preparation?

Yes, the NCERT Solutions provide detailed step-by-step explanations for all questions, making them an excellent resource for exam preparation.

Do the solutions include diagrams for better understanding?

Yes, the solutions include detailed diagrams to help students visualize the problems and understand the geometric concepts better.
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