NCERT Solutions for Class 9 Chapter 10 Maths: Get Free PDF - Embibe
  • Written By Khushbu
  • Last Modified 08-08-2022
  • Written By Khushbu
  • Last Modified 08-08-2022

NCERT Solutions for Class 9 Maths Chapter 10

NCERT Solutions for Class 9 Maths Chapter 10: In this article, we bring students the detailed NCERT Solutions Chapter 10 of Class 9. Our academic experts prepare the solutions provided here at Embibe. Students can download the Class 9 Maths Chapter 10 solutions in PDF format to study offline. Students can use these solutions while solving the exercise questions. Besides that, these solutions will also be very handy for finishing assignments and homework on time.

With all the answers in one place, students can also do their revisions faster. The solutions will also help them to clear all their doubts regarding Class 9 Maths Chapter 10. Embibe offers a wide range of study materials, including PDFs of NCERT books, solution sets and previous year’s question papers. Students can follow these PDFs to enhance their preparations significantly. So, keep reading this article to get the NCERT solutions for Class 9 Maths Chapter 10.

NCERT Solutions for Class 9 Maths Chapter 10: Circles

The NCERT Solutions for Class 9 Maths Chapter 10 involves exercise 10.1, exercise 10.2, exercise 10.3, exercise 10.4, exercise 10.5, and exercise 10.6. All the topics are tabulated below:

ExerciseTopics
10.1Introduction
10.2Circles and its related terms: A Review
10.3Angle Subtended by a chord at a point
10.4Perpendicular from the Centre to a Chord
10.5Circle through three points
10.6Equal Chords and their distances from the Centre
10.7Angle Subtended by an Arc of a Circle
10.8Cyclic Quadrilaterals
10.9Summary

How to Prepare for CBSE Class 9 Maths Circles?

The Class 9 Maths Circles solutions are provided here in a simplified manner that is easy to follow and understand. Once their concepts are clear, solving the exercise questions becomes quite easy. Students can make use of these as they solve the exercise questions.

To boost their performance in the exam, students can solve free Class 9 Maths Circle questions at Embibe. Also, students can take CBSE Class 9 Circles Chapter-wise mock test to test their performance. Finish the chapter in the most effective manner so that students can solve any question asked.

CBSE Class 9 Maths Chapter 10: Important Questions

Some of the important questions from this chapter are as follows:

Important Questions From Circles
  1. Bisectors of angles A, B, and C of a triangle ABC intersect its circumcircle at D, E, and F, respectively. Prove that the angles of the triangle DEF are 90° – (½)A, 90° – (½)B and 90° – (½)C.
  2. In any triangle ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.
  3. Prove that the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals.
  4. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lies on the third side.
  5. Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its center. If the distance between AB and CD is 6, find the radius of the circle.
  6. If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
  7. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.
  8. A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed, and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.
  9. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
  10. Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.
  11. AC and BD are chords of a circle which bisect each other. Prove that
    (i) AC and BD are diameters
    (ii) ABCD is a rectangle.
  12. Prove that a cyclic parallelogram is a rectangle.
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CBSE Class 9 Maths Chapter 10: Summary

In this chapter, students will learn about circles, their related terms, and the properties of a circle. A circle is a collection of points on a plane which are equidistant from a fixed point in the plane. A circle is the locus of points equidistant from a given point. The fixed point is called the centre, while the fixed distance is called the radius.

A circle divides the plane into three parts: inside the circle, on the circle, and the area outside the circle. In this chapter, students will learn some terms related to circles like the centre of a circle, radius, diameter, arcs, and its types – major arc and minor arc, semicircle, chords, cyclic quadrilaterals, segments, and its two types – major segment and minor segment, etc.

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FAQs based on CBSE Class 9 Maths Chapter 10

Q1. What are the topics are covered in NCERT Class 9 Maths Chapter 10?
Ans: The topics involved in the NCERT Class 9 Maths Chapter 10 are as follows:

  • 10.1: Introduction
  • 10.2: Circles and its related terms: A Review
  • 10.3: Angle Subtended by a chord at a point
  • 10.4: Perpendicular from the Centre to a Chord
  • 10.5: Circle through three points
  • 10.6: Equal Chords and their distances from the Centre
  • 10.7: Angle Subtended by an Arc of a Circle
  • 10.8: Cyclic Quadrilaterals
  • 10.9: Summary

Q2. What can I learn from NCERT Class 9 Maths Chapter 10?
Ans:
In this chapter, students will learn about circles, their related terms, and the properties of a circle. Moreover, students will also learn some terms related to circles like the centre of a circle, radius, diameter, arcs, and its types – major arc and minor arc, semicircle, chords, cyclic quadrilaterals, segments, and its two types – major segment and minor segment, etc.

Q3. What is the difference between a chord and a diameter?
Ans: A chord is described as a line segment drawn between any two points in a circle. However, a diameter is drawn at the middle of a circle. It cuts the circle into two halves.

Q4. What are the benefits of using NCERT Solutions for Class 9 Maths Chapter 10?
Ans: The concepts are explained in simple language in the NCERT Solutions for Class 9 Chapter 10 by Embibe. To boost up their performance in the exam, students can solve free Class 9 Maths Circle questions at Embibe. Also, students can take the CBSE Class 9 Circles Chapter-wise mock test to test their performance. These are some of the benefits of using NCERT Solutions for Class 9 Maths Chapter 10.

Q5. Are the NCERT Solutions for Class 9 Maths Chapter 10 easy to understand?
Ans: The NCERT Solutions by Embibe will help students understand the chapter Circle better. The NCERT Solutions for Class 9 Maths Chapter 10 have been explained in a step-by-step manner and detailed manner so that any class 9 student can understand NCERT Solutions for Class 9 Chapter 10.

Q6. How many exercises are present in NCERT Class 9 Maths Chapter 10?
Ans: The NCERT Class 9 Maths Chapter 10 is divided into 9 sections and 6 exercises. The NCERT Solutions for Class 9 Maths Chapter 10 involves exercise 10.1, exercise 10.2, exercise 10.3, exercise 10.4, exercise 10.5, and exercise 10.6.

Also, check-

NCERT SOLUTIONS FOR CLASS 9 MATHS CHAPTER 9NCERT SOLUTIONS FOR CLASS 9 MATHSNCERT SOLUTIONS FOR CLASS 9 MATHS CHAPTER 11
NCERT SOLUTIONS FOR CLASS 9 MATHS CHAPTER 12NCERT SOLUTIONS FOR CLASS 9 MATHS CHAPTER 1NCERT SOLUTIONS FOR CLASS 9

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