NCERT Solutions for Class 10 Maths Chapter 11 Constructions (Ex 11.2)
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Mathematics is a remarkably high scoring subject and the results of Mathematics in the board examinations of Class 10 also have a considerable impact on the choice of academic stream in Class 11. If students work harder, they can easily get good marks in Mathematics. Understanding the concepts is essential because the subject relies on calculation and problemsolving skills. Practice is the key to success in Mathematics.
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ToggleEvery complex and advanced concept and theme in mathematics is built on the foundation of the concepts taught in the class 10 mathematics curriculum. . Students are introduced to several significant concepts in the curriculum of Mathematics for Class 10 that will be extremely important in the later grades. Class 10 Mathematics is significant for board exams and for deepening understanding of the fundamentals of Mathematics because it is a mandatory subject in the curricula of most boards. CBSE Class 10 Mathematics aims to support students as they solidify their understanding of the Mathematical knowledge and abilities they acquired in the primary grades. Students in Class 10 Mathematics are introduced to new mathematical concepts and chapters like trigonometry, which can aid in their comprehension of the practical applications of the concepts they have learned.
Mathematics consists of concepts that are learned through practice. By setting up a study schedule, students can stay on track. Students must adhere to the schedule they determine for themselves on a routine basis. If they do it, students will be able to comprehend fundamental mathematical ideas more quickly. Moreover, before studying for their examinations, students should be aware of the CBSE Class 10 Mathematics syllabus. It will assist students in developing a more effective personal study schedule. Students must also learn how many topics and chapters they must finish during the session. The content of the course should be completed timely so that students have sufficient time for review and practice.
Students must be aware of the pattern of the examination question paper.They must be aware of the examination questions’ quantity and nature. On the day of the examination, it will enable them to spend less time understanding the format of the paper.
Students are required to attempt 14 questions for a total of 40 marks in the CBSE Class 10 Mathematics term 2 Paper. There will be two, three, and fourmark questions. Students will have 2 hours to complete the assignment. As a result, students will need to organise their time to spend two hours carefully trying each question, including time to think about the more difficult ones.
A student can achieve high marks in the Mathematics examination of CBSE Class 10 by using the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2. The majority of the Class 10 test questions can be found in the NCERT textbooks, and for this reason, students are advised to refer to them first. It is the standard textbook for CBSE Mathematics in Class 10. Students must answer every inherent question included in the NCERT books. Students can use the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 if they get hindered while trying to solve a problem. Negligent errors could prove to be detrimental to the conceptual understanding of students. Students should consider these factors as they practise the questions.
If students do not have adequate conceptual understanding, they are more likely to solve problems incorrectly and apply incorrect formulas. An incorrect response is produced by approaching the question incorrectly. These negligent errors could alter the essence of the entire solution. Candidates must respond to questions in a controlled and accurate manner. Students are advised to maintain calmness as they take the secondterm Mathematics examination for CBSE Class 10.
A lot of practise and regular revision are required for the subject of Mathematics. Students will find it difficult to retain the knowledge necessary to solve a problem if they don’t practise Mathematics on a regular basis. There will be 14 subjective questions for term 2 Mathematics. Each step to solving a problem is imperative in the Mathematics paper, so students in Class 10 need to be vigilant and sincere. The mathematical concepts imparted within this chapter will assist students in passing challenging entrance examinations and competitions like the NTSE, SOF Olympiad, and international mathematical olympiad.
The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are available to students in Class 10 for the subject of Mathematics in PDF format. By using the Extramarks website and mobile application, students can access the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 a dependable and trustworthy study resource.
The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 encourage students to be confident in their skills as they prepare for the final examination. Additionally, students can regularly practise related mathematical problems and evaluate their answers by comparing them to NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2. Furthermore, with the help of the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2, students can understand the proper way to respond to Mathematics questions.
Students must carefully read and comprehend the chapter, the subject’s significance, and any subtopics. Understanding the chapter and finishing the final examination preparation are essential. Additionally, students should become familiar with the syllabus before coming up with a plan for final examination preparation. The syllabus is the most important factor in achieving the highest examination grade. Sufficient time must be allocated to ensure that the main subject is covered in the classroom. When preparing for their examinations, students remember that the main examination will last three hours. Additionally, it is recommended that during the examinations, students should always start with the question with the higher score and attempt the questions worth 1 and 2 marks towards the end.
NCERT Solutions for Class 10 Maths Chapter 11 Constructions (Ex 11.2) Exercise 11.2
The NCERT solutions for Class 10 Maths Chapter 11 Exercise 11.2 are available for PDF download. The solutions to all the exercises of the chapter are compiled in one location on the Extramarks educational website and Learning App. These solutions are created by a panel of subject matter experts while following the NCERT and CBSE guidelines. Students can review the entire syllabus and get better marks by practising NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2. Students can use NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 to help them revise the entire syllabus and score higher in their examinations.
The division of a line segment into a given ratio is a concept students will learn in this chapter. A line segment can be divided by measuring its length and then marking the point that divides it in a specific ratio.Students will learn how to divide a line segment into a specified ratio using the compass. As a part of this chapter, students will learn how to create a circle’s tangent. They should be aware that no tangent to a circle can form at a point inside a circle, whereas if a point is outside the circle, there is only one tangent to a circle at this location, which is perpendicular to the point’s radius.
Students can use NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 to understand the chapter fully. Class 10 Chapter 1 of Mathematics must be fully comprehended by students if they are striving to attain excellence in examinations. Moreover, with the help of NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2, students can comprehend the exercises and prepare for the examinations. Additionally, students can check their answers using NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2.
The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are available for download as PDF versions for Class 10 students. In addition to being an excellent resource for students, NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 can also be accessed through the Extramarks website and mobile application.
The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are available for students who need assistance with Exercise 11.2 of Class 10. All students can access trustworthy and dependable educational materials through the learning platform of Extramarks. Furthermore, Extramarks make it simpler to find study materials. The Extramarks website and mobile application offer students in Class 10 access to the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 in PDF format.
The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are based on the introduction to Chapter 11. Students need to understand and use some basic conceptsto complete this exercise. The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 can be found on the Extramarks website, through which students can get academic assistance. The NCERT Solutions for Class 10 Maths, Chapter 11, Exercise 11.2 includes all of the answers to assist students in completing and comprehending this exercise.In order to achieve the best grades on their examinations, students should practise extensively in this chapter.Access NCERT Solutions for Class 10 Maths Chapter 11 – Constructions
Students who want to do well in Class 10 Mathematics must practise the topics covered in the CBSE Mathematics Syllabus a lot. The CBSE 10th Mathematics syllabus contains details about the entire course structure, the weighting of the different units, etc. Students must always have the NCERT Class 10 Mathematics syllabus close at hand when they start their preparation.
The six units that constitute the class 10 mathematics curriculum for the CBSE are Number System, Algebra, Coordinate Geometry, Geometry, Measurement, Statistics, and Probability. The list of all the units that would be a part of the curriculum of the class 10 board exams of Mathematics is provided below. To decide which unit to focus on, students should go over the units and understand the distribution of marks for each.
UNIT  MARKS 
Number system  10 
Algebra  20 
Coordinate Geometry  04 
Geometry  27 
Mensuration  13 
Statistics & Probability  06 
Total  80 
Internal Assessments  20 
Total marks  100 
The Division of A Line Segment, Creation of Tangents to a Circle, Line Segment Bisector, and many other concepts are covered in Chapter 11. In Class 9, students learn the Fundamentals of Construction, including Drawing the Perpendicular Bisector of a Line Segment, Bisecting an Angle, and Constructing Triangles. Students in Class 10 will learn about some more constructions and the reasoning behind them while applying concepts learned in Class 9.
The chapter on Constructions in the NCERT textbook of Mathematics for Class 10 falls under the Geometry category. Geometry has consistently carried a 15mark weightage in the final examinations. The Geometry section’s Construction chapter is a scoring chapter.
When preparing for their examinations, CBSE students should practise Exercise 11.2 Class 10 consistently. There are numerous exercises in this chapter. The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are available on Extramarks in PDF format. Students can study with the aid of NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 at their convenience by downloading it from the Extramarks website and mobile application.
The Construction Class 10 Ex 11.2 is quite challenging, and some students may struggle to complete the practise questions because Exercise 11.2 Class 10 NCERT Solutions is inclusive of several difficult topics. The NCERT books contain comprehensive exercises pertaining to Chapter 11. It is noteworthy that, in order to assist with the solution of the exercise, students can use the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2.
Students may ask questions about the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 during the live doubtsolving sessions that Extramarks offers on their website and Learning App. The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 can be used by students who are facing challenges while learning Chapter 11. Students can access the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 and begin working on their solutions.
For students in Class 10, Chapter 11 presents a number of mathematical concepts that could prove difficult to understand. Practising formulas is crucial for understanding them. This chapter has plenty of exercises to help students thoroughly clear up any questions they may have. The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are available on Extramarks, one of the best elearning platforms.
The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are available on the Extramarks digital learning portal. Students looking for the best educational resources are already in the right place. The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are written in clear and simple language that is easy to comprehend. The PDF file of NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 is available on the Extramarks website.
NCERT Solutions for Class 10 Maths Chapter 11 Constructions Exercise 11.2
In terms of the academic careers of students, the Class 10 examinations typically occupy a significant position. It becomes even more crucial to understand a subject like Mathematics, which cannot be comprehended through retention alone and can not be passed without adequate comprehension of vital concepts. However, grades alone are not important; understanding the concepts is also necessary because doing so will benefit students for the rest of their academic endeavours. The NCERT Solutions for Class 10 Maths, Chapter 11, Exercise 11.2 help students understand the answers to the questions in the books.
As students may know, Mathematics is not an easy subject and is entirely based on concepts. However, if students understand the characteristics of every fact, they can easily score well in the subject. Students who want to do well in the Class 10 board exams are advised to practise exercises from each chapter. To make it simpler for the students, the NCERT Solutions for Class 10 Mathematics explain every detail. Students studying can learn the proper way to answer the questions that will be asked of them in the board examination by using the solutions created using the NCERT guidelines.
The extremely proficient panel of subjectmatter experts at Extramarks has created the NCERT Solutions for Chapter 11 of Class 10 Mathematics. When students read through these NCERT Solutions for Chapter 11 for the CBSE Class 10 board exams, they will thoroughly understand how to construct geometric figures.
This chapter begins with the theme of Splitting a Line Segment into a Predetermined Ratio. The construction of a triangle similar to a given triangle is done next, followed by tangents to a circle from a point outside. Students can learn about the creation of various geometric figures from this chapter. Students can learn how to divide a line segment and comprehend the creation of tangents to a circle from the two exercises in this chapter. The solutions crafted by Extramarks provide examples and an easytounderstand explanation of construction methods and steps to help students understand them. The Basic Proportionality Theorem also referred to as the Thales Theorem, is covered in this chapter.
Exercise 11.1 consists of a total of 7 questions. These problems would help students understand how to construct line segments, divide them into parts according to a given ratio, and construct various triangles. For instance, students must construct Isosceles Triangles to solve some of the sums in this exercise. Students should solve and practise all the problems provided in this exercise to construct geometric figures more accurately on the examination.
Chapter 11 of Math for Class 10 second exercise consists of 7 problems related to Construction. These include the constructions of tangents, lines, rightangled triangles, and more. Theorems and concepts related to triangles, circles, and other geometric figures will be used by students to support some of the constructions.
Central Board of Secondary Education (CBSE) students can easily download the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 from the Extramarks website and mobile application. The solutions are provided by highly knowledgeable subject specialists of Mathematics. Students may use NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 to complete all the tasks in Exercise 11.2.Students can access the top study resources for NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 on the Extramarks website. Students should go over NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 again to strengthen their understanding of Mathematics Class 10 Chapter 11 in both Hindi and English.For future reference, NCERT Solutions for Class 10 Maths, Chapter 11, Exercise 11.2 can be downloaded in PDF format
Q.1 Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Ans.
$\begin{array}{l}\mathrm{Steps}\mathrm{of}\mathrm{Construction}:\\ \text{Step 1: Draw a circle of radius 6 cm with centre at point O.}\\ \text{Locate a point P, 10 cm away from O, and join O and P.}\\ \text{Step 2:}\mathrm{Bisect}\text{OP. Let M be the midpoint of OP.}\\ \text{Step 3:}\mathrm{Draw}\text{a circle with centre at M and MO as radius. Q and}\\ \text{R are points of intersections of this circle with the circle}\\ \text{having centre at O.}\\ \text{Step 4: Join PQ and PR. PQ and PR are the required tangents.}\\ \mathrm{The}\text{lengths of tangents PQ and PR are 8 cm each.}\end{array}$
Q.2 Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
Ans.
$\begin{array}{l}\mathrm{Steps}\mathrm{of}\mathrm{Construction}:\\ \text{Step 1: Draw a circle of radius 4 cm with centre at point O.}\\ \text{Draw anothe circle of radius 6 cm with centre at}\\ \text{point O. Locate a point P on this circle and join OP.}\\ \text{}\\ \text{Step 2:}\mathrm{Bisect}\text{OP. Let M be the midpoint of OP.}\\ \text{Step 3:}\mathrm{Draw}\text{a circle with centre at M and MO as radius. Q and}\\ \text{R are points of intersections of this circle with the circle}\\ \text{having centre at O.}\\ \text{Step 4: Join PQ and PR. PQ and PR are the required tangents.}\\ \mathrm{On}\mathrm{measuring}\mathrm{we}\mathrm{get}t\mathrm{he}\text{lengths of tangents PQ and PR are 4.5 cm each.}\end{array}$
$\begin{array}{l}\mathrm{In}\text{}\mathrm{\Delta}\text{\hspace{0.17em}PQO, we have}\\ \angle \text{PQO}=90\mathrm{\xb0}\text{[PQ is a tangent]}\\ \text{PO}=\text{\hspace{0.17em}}6\text{cm [Radius of the circle]}\\ \text{QO}=4\text{cm [Radius of the circle]}\\ \mathrm{By}\text{applying Pythagoras theorem in}\mathrm{\Delta}\text{\hspace{0.17em}PQO},\text{we have}\\ {\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}PQ}}^{2}+{\mathrm{QO}}^{2}={\mathrm{OP}}^{2}\\ \mathrm{or}{\text{\hspace{0.17em}PQ}}^{2}+{4}^{2}={6}^{2}\\ \mathrm{or}{\text{\hspace{0.17em}PQ}}^{2}=3616=20\\ \mathrm{or}\text{\hspace{0.17em}PQ}=\sqrt{20}=2\sqrt{5}=4.5\text{cm approx.}\\ \text{We know that PQ}=\mathrm{PR}\text{as these tangents are drawn from}\\ \text{a single point P.}\\ \mathrm{Therefore},\text{PQ}=\mathrm{PR}=4.5\text{cm approx.}\end{array}$
Q.3 Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Ans.
$\begin{array}{l}\mathrm{Steps}\mathrm{of}\mathrm{Construction}:\\ \text{Step 1: Draw a circle of radius 3 cm with centre at point O.}\\ \text{Step 2: Take one of its diametre, RS, and extend it on both}\\ \text{sides. Locate two points P and Q on this diametre}\\ \text{such that OP}=\mathrm{OQ}=7\text{cm}.\\ \text{Step 3:}\mathrm{Bisect}\text{OP and OQ. Let T and U be the midpoints of}\\ \text{OP and OQ respectively.}\\ \text{Step 4: Taking T and U as centres and OT and OU as radii,}\\ \text{d}\mathrm{raw}\text{two circles. These two circles will intersect}\\ \text{the circle at points V, W, X, Y. Join PV, PW, QX and QY.}\\ \text{These are the required tangents.}\end{array}$
Q.4 Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
Ans.
$\begin{array}{l}\mathrm{Steps}\mathrm{of}\mathrm{Construction}:\\ \text{Step 1: Draw a circle of radius 5 cm with centre at point O.}\\ \text{Step 2: Take a point A on circumference of the circle and join}\\ \text{OA. Draw a perpendicular to OA at point A.}\\ \text{Step 3: Draw a radius OB, making an angle of 120\xb0 with OA.}\\ \text{Step 4:}\mathrm{Draw}\text{a perpendicular to OB at point B. Let both the}\\ \text{perpendiculars intersect at point P. PA and PB are}\\ \text{the required tangents at an angle of 60\xb0.}\end{array}$
Q.5 Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Ans. Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
Q.6 Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
Ans.
As per given information, we have the following figure.
$\begin{array}{l}\mathrm{Steps}\mathrm{of}\mathrm{Construction}:\\ \text{Step 1: Join AE and bisect it. Let F be the midpoint of AE.}\\ \text{Step 2: Taking F as centre and FE as its radius, draw a circle}\\ \text{which will intersect the other circle at points B and G.}\\ \text{Join AG. AB and AG are the required tangents.}\end{array}$
Q.7 Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
Ans.
$\begin{array}{l}\mathrm{Steps}\mathrm{of}\mathrm{Construction}:\\ \text{Step 1: Draw a circle with the help of a bangle.}\\ \text{Step 2: Take a point P outside this circle and take two}\\ \text{chords QR and ST.}\\ \text{Step 3: Draw perpendicular bisectors of QR and ST. Let}\\ \text{the perpendicular bisectors intersect each other}\\ \text{at point O.}\\ \text{Step 4: Join OP and bisect it. Let U be the midpoint of OP.}\\ \text{Taking U as centre, draw a circle of radius OU,}\\ \text{which intersects the previous circle at V and W.}\\ \text{Join PV and PW.}\\ \text{PV and PW are the required tangents.}\end{array}$
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FAQs (Frequently Asked Questions)
1. What objective questions are asked in Section A of the question paper of Class 10 Mathematics?
The objectivetype questions, which constitute Section A of the Mathematics examination of Class 10 come in various formats, including multiplechoice, fillintheblank, and very short answers.
2. How can students achieve excellence in the Mathematics examination of Class 10?
Students should consistently practice the problems from the NCERT textbook if they want to do well on their class 10 Mathematics examination. They must be completely familiar with each chapter’s syllabus and the topic weightage allotted to each chapter.
3. Where can students conveniently find NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2?
The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 can be accessed on the Extramarks website and mobile application in PDF format. The Class 10 Maths Chapter 11 Exercise 11.2 NCERT Solutions are presented. The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are designed by highly experienced mentors of Mathematics.
4. What are the advantages of using Extramarks’ NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2?
The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 can be found on the Extramarks website and mobile application, and are very trustworthy and authentic learning resources. The NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 are created by experienced educators of Mathematics and are regularly updated to reflect curriculum changes. Additionally, students can peruse the NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 offline by downloading these in PDF format.