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NCERT Solutions for Class 10 Maths Chapter 10 Ex 10.2

NCERT Solutions for Class 10 Maths Chapter 10 Ex 10.2 are prepared by expert Maths faculty at askIITians. Exercise 10.2 of Chapter 10 Circles is based on theorems related to the number of tangents from a point on a circle. There are 13 questions in this exercise whose stepwise solutions are given by askIITians Maths experts. You can download these solutions in PDF form and refer to them whenever you want. This way you can study independently, resolve your doubts on your own and prepare well for Class 10 Maths board exams. 

 

About Class 10 Maths NCERT Chapter 10 Circles Ex 10.2

There are only two exercises in the Circles chapter. The second exercise is based on the number of tangents from a point on a circle. It is an important exercise as you will practice different theorems in it. Here are some noteworthy points regarding Ex 10.2 that you must keep in mind before solving the exercise: 

Circle: A circle is a collection of all points in a plane that are at a constant distance (radius) from a fixed point (centre or origin). 

Tangent: A tangent to a circle is the line that intersects the circle at only one point. 

The common point of the tangent and the circle is called the point of contact. Consider the following diagram: 

Here, the length of the segment of the tangent from the external point P and the point of contact with the circle is called the length of the tangent from the point P to the circle.

Theorem: The lengths of tangents drawn from an external point to a  circle are equal.

In the figure given above, length of PQ = length of PR. 

Also, ∠ OPQ = ∠ OPR. Therefore, OP is the angle bisector of ∠ QPR, i.e., the centre lies on the bisector of the angle between the two tangents.

Types of questions included in NCERT Class 10 Maths Chapter 10 Ex 10.2:

 

Ex 10.2 Q1 - Q3: The first three questions of this exercise are multiple-choice questions where you have to choose the correct option and also give a justification for your answer. Many students face difficulty in giving the reasoning properly. Our NCERT Solutions will help you in this case. 

Ex 10.2 Q4 and Q5: These two questions require you to prove the given statement. In Q4 you have to prove that the tangents drawn at the ends of a diameter of a circle are parallel. In Q5, you have to prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Ex 10.2 Q6: In this question, you are given that the length of a tangent from a point A at a distance of 5 cm from the centre of the circle is 4 cm. You have to find the radius of the circle. This question is based on the application of the theorem given in this exercise. 

Ex 10.2 Q7: In this question, it is given that two concentric circles are of radii 5 cm and 3 cm. You have to find the length of the chord of the larger circle which touches the smaller circle.

Ex 10.2 Q8: In this question, you are given a diagram of a quadrilateral ABCD that circumscribes a circle. You have to prove that AB + CD = AD + BC. To know how to solve this question step by step, refer to our NCERT Solutions for Class 10 Maths Chapter 10 Ex 10.2. 

Ex 10.2 Q9: This is again a diagram-based question where you are given that XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with the point of contact C intersecting XY at A and X′Y′ at B. You have to prove that ∠ AOB = 90°.

Ex 10.2 Q10 and Q11: Both these questions require you to prove the given statements. In question 10, you have to prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre. In Q11, you have to prove that the parallelogram circumscribing a circle is a rhombus.

Ex 10.2 Q12: This is a diagram-based question in which you are given a triangle that circumscribes a circle. You must study the diagram carefully to solve this question correctly. Our NCERT Class 10 Maths Solutions will help you understand how to solve this question. 

Ex 10.2 Q13: In this question, you have to prove the given theorem: opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. 

Download Free NCERT Solutions for Class 10 Maths Chapter 10 Ex 10.2

As you can see that most of the questions in this exercise require you to prove statements based on the concepts that you have learned in this chapter. This could be a little tricky but with practice, you can master how to solve such questions in the board examination. Our NCERT Solutions are your ultimate guide at every point.

 

Key features of NCERT Class 10 Maths Solutions for Chapter 10 Circles Ex 10.2:

  • All the NCERT Solutions are prepared by experienced, qualified, professional teachers. You can rely on these solutions one hundred percent. 
  • These solutions are based on the latest CBSE Class 10 Maths Syllabus and exam pattern so you can prepare the best for your Maths board exam. 
  • The NCERT Solutions help in solidifying your concepts related to tangents of a circle so that you can answer all types of questions in the exam. 
  • The solutions are free to download in PDF form so that you can access them at any time and practice this chapter at your own pace. 

Download exercise-wise NCERT Solutions for Class 10 Maths Chapter 10 Circles and start practising: 

  • NCERT Solutions for Class 10 Maths Chapter 10 Ex 10.1
  • NCERT Solutions for Class 10 Maths Chapter 10 Ex 10.2

NCERT Solutions for Class 10 Maths Chapter 10 Ex 10.2 FAQs

  1. How many exercises are there in NCERT Class 10 Maths Chapter 10 Circles? 

The Circles chapter of NCERT Class 10 Maths includes 2 exercises. The first exercise includes 4 questions and the second exercise includes 13 questions. 

  1. Is NCERT Class 10 Maths Chapter 10 Circles Ex 10.2 difficult? 

You will find this exercise difficult if you have not understood the concepts of the chapter. Use our NCERT Solutions for this exercise to resolve your doubts and master the concepts of this exercise. We guarantee that you will not find it difficult. 

  1. Are there any study resources to prepare the Class 10 Maths Circles Chapter? 

The askIITians Maths experts have prepared revision notes, mind maps, flashcards, previous year question papers, and extra questions to help you revise the Circles chapter thoroughly. 


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