NCERT Solutions for Exercise 10.2 Class 9 Maths Chapter 10 - Circles

NCERT Solutions for Exercise 10.2 Class 9 Maths Chapter 10 - Circles

NCERT Solutions for Class 9 Maths chapter 10 exercise 10.2 is about angle subtended by a chord at a point. A circle is a two-dimensional geometrical form in which all points on the surface of the circle are equidistant from the radius, which is the centre point. A circle's chord is the line segment that connects two locations on its circumference. You will see that the angles subtended by two or more equal chords of a circle at the centre are equal if you draw two or more equal chords of a circle and determine the angles they occupied in the centre. In the NCERT solutions for Class 9 Maths chapter 10 exercise 10.2, we will cover the theorems pertaining to the angle subtended by a chord at a point in depth. The following exercise are also included in NCERT book Class 9 Mathematics chapter 10 exercise 10.1.

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  • Circles Exercise 10.1

  • Circles Exercise 10.3

  • Circles Exercise 10.4

  • Circles Exercise 10.5

  • Circles Exercise 10.6

Circles Class 9 Chapter 10 Circles Exercise: 10.2

Q1 Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Answer:

Given: The two circles are congruent if they have the same radii.

To prove: The equal chords of congruent circles subtend equal angles at their centres i.e. BAC= QPR

Proof :


In ABC and PQR,

BC = QR (Given)

AB = PQ (Radii of congruent circle)

AC = PR (Radii of congruent circle)

Thus, ABC PQR (By SSS rule)

BAC= QPR (CPCT)

Q2 Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Answer:

Given : chords of congruent circles subtend equal angles at their centres,

To prove : BC = QR

Proof :

In ABC and PQR,

BAC= QPR (Given)

AB = PQ (Radii of congruent circle)

AC = PR (Radii of congruent circle)

Thus, ABC PQR (By SAS rule)

BC = QR (CPCT)

More About NCERT Solutions for Class 9 Maths Exercise 10.2

As we know NCERT solutions for exercise 10.2 Class 9 Maths chapter 10 is about angle subtended by a chord at a point. But along with the topics about circles such as chords, arc, major arc, minor arc, semicircle, we have also used the information about the congruence of the triangle which we have covered in Class 9 chapter 7 triangle. Some of the rules and properties which we are using are side - side - side rule, side - angle - side rule and there are some theorems which are covered before Class 9 Maths chapter 10 exercise 10.1 these theorems are at the centre of a circle, equal chords subtend equal angles. If the angles subtended by the chords of a circle at its centre are equal, then the chords are equal, as well as the theorem.

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Also Read| Circles Class 9 Notes

Benefits of NCERT Solutions for Class 9 Maths Exercise 10.2

  • The circle is an important part of geometry and there are a lot of applications of circles in whole geometry

  • Chapter 10 exercise 10.2 in Class 9 Maths presents a wide range of problems that can be based on angle subtended by a chord at a point.

  • NCERT Class 9 Maths chapter 10 exercise 10.2, will be helpful for the Class 10 chapter 10 circle, as Class 10 chapter 10 circle is an extension of Class 9 Maths chapter 10

  • NCERT Class 9 Maths chapter 10 exercise 10.2, will be base for the Class 11 chapter 11 conic section

  • NCERT Class 9 Maths chapter 10 exercise 10.2, will be helpful in JEE Main (joint entrance exam) as the conic section is a major part of the syllabus and the circle is a part of the conic section section

Also, See

  • NCERT Solutions for Class 9 Maths Chapter 10

  • NCERT Exemplar Solutions Class 9 Maths Chapter 10

NCERT Solutions of Class 10 Subject Wise

  • NCERT Solutions for Class 9 Maths

  • NCERT Solutions for Class 9 Science

Subject Wise NCERT Exemplar Solutions

  • NCERT Exemplar Class 9 Maths
  • NCERT Exemplar Class 9 Science