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NCERT Solutions for Class 10 Maths Chapter 10: Circles - Exercise 10.1

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NCERT Solutions for Class 10 Maths Chapter 10 Circles

Free PDF download of NCERT Solutions for Class 10 Maths Chapter 10 Exercise 10.1 (Ex 10.1) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 10 Maths Chapter 10 Circles Exercise 10.1 Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register and get all exercise NCERT Book Solutions in your emails. Subjects like Science, Maths, English will become easy to study if you have access to Class 10 Science NCERT Solutions, Maths solutions, and solutions of other subjects that are available on Vedantu only.



Class:

NCERT Solutions for Class 10

Subject:

Class 10 Maths

Chapter Name:

Chapter 10 -  Circles

Exercise:

Exercise - 10.1

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2024-25

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes



Important Formulas Related to Circles

Chapter 10 of the Class 10 maths syllabus is on Circles. This chapter is one of the most significant chapters when it comes to geometry and construction. The chapter on circles is an elaborate one and usually takes some time to master. Let us begin with some basic formulas. The following is a list of 3 important formulas that are related to circles.

  • Diameter of a circle = D = 2 × r (where r is the radius of the given circle)

  • Circumference of a circle = C = 2 × π × r (where r is the radius of the given circle)

  • Area of a circle = A = π × r2 (where r is the radius of the given circle)

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Access NCERT solution for Class 10 Maths Chapter 10 – Circles

EXERCISE NO: 10.1

1.How many tangents can a circle have?

Ans: A circle can have an infinite number of tangents. A circle is made of infinite points and from each point, a tangent can be formed.


2.  Fill in the blanks :

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

Ans:  A tangent to a circle intersects it in exactly one point.

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

Ans:  A line intersecting a circle in two points is called a secant.

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

Ans:  A circle can have two parallel tangents at the most opposite to one another.

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

Ans:  The common point of a tangent to a circle and the circle is called the Point of Contact.


3. A tangent PQ at a point P of a circle of radius \[\text{5cm}\] meets a line through the centre O at a point Q so that \[\text{OQ = 12cm}\]. Length of PQ is :

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

(B) \[\text{13}\]cm

(C) \[\text{8}\text{.5}\] cm

(D)\[\sqrt{\text{119}}\]

Ans: According to the Pythagoras Theorem: \[PQ=\sqrt{\left( O{{Q}^{2}}-\left. O{{P}^{2}} \right) \right.}\]

OQ = \[\text{12}\]cm,  OP = \[\text{5}\]cm

Because, 

\[PQ=\sqrt{\left( O{{Q}^{2}}-\left. O{{P}^{2}} \right) \right.}\]

\[=\sqrt{\left( {{12}^{2}}-\left. {{5}^{2}} \right) \right.}\]

\[=\sqrt{144-25}\]

\[=\sqrt{119}\]cm.

Hence, (D) is the answer.


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

Ans: From the Given Figure below,


Circle


Let ‘l’ be the given line and a circle with centre O is drawn. 

  • A tangent to the circle from point B is drawn \[\parallel \] to line ‘l’.

  • CD is drawn \[\parallel \] to line ‘l’ and is the secant.


NCERT Solutions for Class 10 Maths Chapter 10 Circles Exercise 10.1

Opting for the NCERT solutions for Ex 10.1 Class 10 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 10.1 Class 10 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 10 students who are thorough with all the concepts from the Subject Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 10 Maths Chapter 10 Exercise 10.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 10 Maths Chapter 10 Exercise 10.1, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

Do not delay any more. Download the NCERT solutions for Class 10 Maths Chapter 10 Exercise 10.1 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.


NCERT Solutions for Class 10 Maths PDFs (Chapter-wise)