NCERT Solutions for Class 9 Maths Chapter 10 Circles (Ex 10.4) Exercise 10.4

One of the most difficult classes a student faces during schooling is Class 9. It prepares students for the more difficult subjects they will study in Class 10 as well as in higher classes. Additionally, it is a lot more difficult than what students in Class 8 were being taught. Board exams are taken in Class 10 by students who attend schools affiliated with the Central Board of Secondary Education (CBSE). But comprehending the ideas covered in Class 10 requires a thorough understanding of the ones covered in Class 9. Board exams are a difficult and unfamiliar experience for students.  This means that students need to have a solid understanding of the concepts covered in Class 9. To fully understand the concepts they have learned, they should not only read the chapters in their entirety but also practice a lot of relevant questions. This can be a huge benefit when students take their annual examinations towards the end of the year. Knowing the various different questions that can be found on exams will help students answer more questions on the test. As a result, they might be able to correctly answer more questions, which might help them perform better on exams.

One of the most challenging subjects for students to master is Mathematics. Class 9 is a crucial year for students because it lays the foundation for their future academic careers. The majority of students struggle with the incredibly intimidating combination of Mathematics and Class 9. However, if it is learned and taught properly, Mathematics can develop into a really fascinating subject. Students across all boards of education in the nation struggle with this subject. The CBSE syllabus for Mathematics covers topics that are logic- and concept-focused, in contrast to other subjects. Once they are able to understand the concepts, students can perform well on their exams. The Extramarks platform can assist Class 9 students at that point. Students can use interactive learning resources from Extramarks made by experts in the field to aid in their understanding of the concepts more easily and effectively. Students need a variety of resources, such as NCERT solutions, to prepare for their exams. Hence, Extramarks provides NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4. With the help of the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, students can comprehend the various types of questions that appear on the question paper and get ready for the annual exams. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, can teach students effective strategies for responding to the question paper. In order to perform well on exams, it is essential for students to practice with NCERT solutions, such as the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4.

NCERT Solutions for Class 9 Maths Chapter 10 Circles (Ex 10.4) Exercise 10.4

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Access NCERT Solution for Class 9 Maths Chapter 10 – Circles

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NCERT Solution Class 9 Maths of Chapter 10 All Exercises

The most crucial resource for reviewing the chapter for annual exams is NCERT exercises. Therefore, it is frequently suggested that students solve the exercises in NCERT textbook’s. Chapter 10 on Circles includes six exercises in total. There are several challenging questions in these exercises. The right answers to the questions are also required to cross-check their answers. By using the NCERT solutions, students can get the support they require as they get ready for the annual exams. Using the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, students can apply the concepts from the chapter in a clear and detailed way. Highly skilled and experienced teachers prepare the thorough and faultless NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4. These solutions were developed with Class 9 students’ thinking skills in mind. The difficult problems in this lesson have been split up into smaller, more manageable chunks to make accurately solving the questions easier. The importance of detailed, step-by-step answers is typically emphasized by teachers. Hence, the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 should be carefully followed by students for the best outcomes in exams. Since many of the theorems provided in the NCERT textbook are difficult for students to understand and remember, they are unable to use them to answer the exercises’ questions. However, if students practice using the stepwise solutions in the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, it will be easier for them to remember the theorems and use them correctly.

NCERT Solutions for Class 9 Maths Chapter 10 Circles (Ex 10.4) Exercise 10.4

The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, have been written by a team of experts in a way that is engaging and simple for students to understand. Class 9 Maths Chapter 10 Exercise 10.4 is one of the most challenging exercises. However, if students use the detailed instructions in the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, they can easily complete the problems in this exercise. If students solve Maths Class 9 Chapter 10 Exercise 10.4 completely, they will also be able to solve the problems in the exercises that come after. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, are helpful for students making preparations for their exams since they are written in straightforward and simple language that any student can fully grasp. The relevant examples and explanations are provided in the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4. This increases students’ confidence and helps them do better on the exams. By providing sufficient examples for practice, it helps them acquire an understanding of the concepts of each topic. Students will not need to search elsewhere for the topics covered in the curriculum or the distribution of marks because the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 have been organised in accordance with the latest CBSE syllabus and guidelines. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, have been written in a step-by-step manner to help students earn the maximum possible marks in the exams. Students must divide complex problems into manageable components in order to solve them quickly. This issue is resolved by having access to the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4. By working through the NCERT textbook exercises, students gain more self-assurance and improve their understanding of even the most challenging topics. Students should also compare their answers to the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 offered by Extramarks for self-evaluation and improvement.

NCERT Solutions for Class 9

In addition to the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, NCERT solutions for other chapters and subjects are also accessible on Extramarks. Students can find thorough NCERT solutions for each of the 15 chapters in the NCERT Mathematics textbook. The answers to the exercises’ questions are also provided in detail. NCERT exercises are frequently given to students as part of their homework by their teachers. When attempting to solve the problems, students run into various hurdles. They sometimes fail to complete their assignments. The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, can help students complete their assignments. After finishing their assigned homework on time, students can move on to their scheduled lessons. They will be able to complete their coursework on time due to this. Due to the fact that these solutions are written in a simple language, students who lack much practice with the exercises can also easily understand the solutions and effectively implement the suggested methods of solving the problems. On Extramarks, Class 9 students can find NCERT solutions for a variety of subjects, not just Mathematics. Students can complete their homework in all subjects taught at their school by using the NCERT solutions available on Extramarks.

CBSE Study Materials for Class 9

To ace the annual exams in Mathematics, students can use a range of study materials from Extramarks. This includes worksheets that are organised by chapters to assist students in understanding every topic covered in the CBSE curriculum. Extramarks also provides a tonne of key questions from each chapter to help students get accustomed to the wide range of problems that might be covered on the test. Students can take the help of visual animations for their studies. Visual animations greatly help in a deeper understanding of the material, which improves the effectiveness of studies. On the Extramarks website, students can access CBSE sample question papers for test preparation. Besides that, they can review all of the previously studied topics with the assistance of the revision notes. Extramarks also has CBSE past years’ papers for practice prior to the exams. It also gives the solutions to these question papers. Along with that, the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 are accessible on Extramarks. On the Extramarks mobile application and website, students can access the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 and download and print them for offline access.

CBSE Study Materials

Class 9 CBSE students need to have access to the best study materials if they want to perform well on the exams. A three-pronged learning-practice-testing strategy is used by Extramarks to help CBSE students perform their best in exams. To teach students all the topics on the CBSE curriculum, the best instructors in India are available at Extramarks. There are a variety of study materials for assistance. Each lesson can be better understood by students if they make use of these study materials. With the aid of these study materials, self-study is made simple. With the help of Extramarks, students can independently learn new topics and gauge how well they are prepared for exams. Students can have access to weekly tests as well as practice tests. They can evaluate their preparedness using adaptive assessments with increasing difficulty levels. The Learning App can be used to track students’ progress. They will be able to identify where they need to make improvements after receiving a thorough evaluation of their performance. Students can also use the NCERT solutions, such as the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4, to complete the NCERT exercises, which are essential for the exams. Students should practice the sample papers and past years’ papers before the annual exams to become comfortable answering questions.

Q.1 Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Ans

Let the assumed figure is as given below:

  Given:Radius OA=5 cm, O’A=3 cm and OO’=4 cm.To find: AB Let OC=x cm and O’C=(4−x) cm In ΔACO, ∠ACO=90°        By Pythagoras theorem, OA2=AC2+OC2                52=AC2+x2⇒      AC2=25−x2       ...(i) In ΔACO‘, ∠ACO‘=90°          By Pythagoras theorem, O’A2=AC2+O‘C2                 32=AC2+(4−x)2⇒        AC2=9−(4−x)2        ...(ii)From equation(i) and equation(ii), we have       25−x2=9−(4−x)2⇒    25−x2=9−(16−8x+x2)⇒    25−x2=9−16+8x−x2⇒              25=−7+8x⇒       25+7=8x⇒           x=328                 =4 cmSubstituting value of x in equation(i), we get              AC2=25−42                    =25−16                    =9⇒           AC=9=3Since, OO’ is perpendicular bisector of AB.So,             AB=2×AC                      =2×3=6 cmThus, the length of common chord is 6 cm.

Q.2 If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Ans

Given:Chord AB= Chord CD, both chords intersect at R.To prove:AR=RC and RB=RDConstruction: Draw OP⊥AB and OQ⊥CD. Join OR.Proof:In ΔOPR and ΔOQR,            OP=OQ       [Equal chords are equidistant.]         ∠OPR=∠OQR   [Each 90°]               OR=OR        [Common]      ∴ΔOPR≅ΔOQR   [By R.H.S.]So,       PR=QR   ...(i)   [By C.P.C.T.]Since,      PB=QD   ...(ii)   [Perpendicular from centre bisects the chord.]Subtracting equation (i) from equation(ii),​ we get         PB−PR=QD−QR⇒     RB=RD     ...(iii)∵      AB=CD    ...(iv)[Given]Equation(iv)−equation(iii), we get       AB −RB=CD−RD⇒          AR=RCand RB=RD.      Hence Proved.

Q.3 If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Ans

Given:Chord AB= Chord CD, both chords intersect at R.To prove:∠ORA=∠ORCConstruction: Draw OP⊥AB and OQ⊥CD. Join OR.Proof:In ΔOPR and ΔOQR,OP=OQ[Equal chords are equidistant.]   ∠OPR=∠OQR [Each 90°]          OR=OR[Common]∴ΔOPR≅ΔOQR [By R.H.S.]So,     ∠ORA=∠ORC [By C.P.C.T.]Hence Proved.

Q.4 If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).

Ans

Given: Two concentric circles with centre O. A common chord intersect these circles at AD and BC. To prove: AB=CD Contruction: Draw OP⊥AD MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@B685@

Proof:Since, perpendicular from centre to chord of circle bisects the chord. So,                      AP=PD       …(i)         and   BP=PC       …(ii)     Subtracting equation(i) from equation(ii), we get               BP−AP=PC−PD⇒                  AB=CD                                     Hence proved.

Q.5 Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?

Ans

Given:Radius of circular park is 5 m, distance between Reshma and Salma(AB) and distance between Salma and Mandeep (BC) is equal to 6 m eachTo Find: Distance between Reshma and Mandeep i.e., AC.Proof:In ΔODC, ∠ODC=90°        So, by Pythagoras Theorem,            OC2=OD2 + DC2            DC2=OC2− OD2            DC2=52−x2     ...(i)           In ΔBDC, ∠BDC=90°       So, by Pythagoras Theorem,            BC2=BD2 + DC2            DC2=BC2− BD2            DC2=62−(5−x)2   ...(ii)From equation(i) and equation(ii), we get              52−x2=62−(5−x)2⇒        25−x2=36−25+10x−x2⇒        25−11=10x⇒             x=1410=1.4Substituting value of x in equation(i), we get            DC2=52−(1.4)2                      =25−1.96                  =23.04              DC=23.04                  =4.8 mThus, AC=2 DC              =2×4.8 m              =9.6 mTherefore, the distance between Reshma and Mandeep is 9.6 m.

Q.6 A circular park of radius 20 m 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 each other. Find the length of the string of each phone.

Ans

Let A, B and C be the positions of Ankur, Syed and David respectively.Radius of circle is 20 m.AD is median of triangle. O is centre of circle as well as intersection point of medians too. Let each side of ΔABC  be 2x.Since, cetroid divides a median in 2:1, then      AOOD=21⇒20OD=21⇒      OD=202=10 mTherefore, AD=20+10=30ar(ΔABC)=12×BC×AD             =12×2x×30             =30x m2In ΔBOD, ∠ODB=90°So, by Pythagoras theorem,          OB2=OD2+BD2       (20)2=(10)2+x2             x2=400−100                =300⇒        x=300               =103So,   BC=2x            =2×103             =203Thus, the length of the string of each phone is 203 m.

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FAQs (Frequently Asked Questions)

1. Where can Class 9 students find the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4?

On the Extramarks website and mobile app, students can find the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4. They  can access and download the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 online in PDF format. This  offers them offline access to the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 so that they can use them whenever and wherever they want without having an internet connection.

2. Which exercise is covered by the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4?

Exercise 10.4 Class 9 Maths is covered in the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4.

3. What topics and theorems are covered in the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4?

The NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 cover the topic Equal Chords and Their Distances from the Centre. These solutions completely solve all the questions in Class 9 Maths 10.4 covering Theorems 10.6 and 10.7.

4. Do the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4 help in understanding the topics covered in this chapter?

Students in Class 9 who are preparing for their annual exams need to practice NCERT exercises on a regular basis. To prepare for the exams, students can use learning resources like the NCERT Solutions For Class 9 Maths Chapter 10 Exercise 10.4. Just simply giving answers will not help secure complete marks. Students must know the procedures used to arrive at the answer. This will help them solve questions easily on the exams.