NCERT Solutions for Constructions Exercise 11.2 Class 10 Maths

NCERT Exercise 11.2 Class 10 Maths Solutions consists of detailed and step-wise answers from the chapter ‘Constructions’. These NCERT solutions from Exercise 11.2 Class 10 Maths provide students with a complete strategy for preparing for the upcoming exams. These solutions designed by subject experts boost the exam preparations of the students and clear their doubts.

Students studying regularly for the exam will find these solutions from NCERT Exercise 11.2 Class 10 Maths relatively easy to understand and improve their logical thinking. Solving the NCERT Exercise 11.2 Class 10 Maths Solutions will enhance the students’ problem-solving skills and help them ace the exams with ease. Students must start practising the exercise questions to help build their knowledge.

NCERT Exercise 11.2 Class 10 Maths Solutions: Overview

The NCERT Exercise 11.2 Class 10 Maths Solutions is crucial from an exam point of view and covers major topics like dividing a line segment and constructing tangents to a circle. Besides, the solutions are provided in PDF form in the article so that students can study them offline. Before jumping into more details, let’s have an overview of the NCERT Exercise 11.2 Class 10 Maths Solutions:

NCERT Exercise 11.2 Class 10 Maths Solutions: PDF

Students must keep practising the NCERT Exercise 11.2 Class 10 Maths Solutions as the questions are prepared by experienced teachers based on the CBSE curriculum. By solving the Exercise 11.2 Class 10 Maths solutions, students understand the complex concepts and score more in the examinations. The NCERT in-text questions also help students with revision and are available for on Embibe.

Students can easily download the PDF at their convenience or study them directly from Embibe. The detailed solutions with step-wise explanations are prepared with the utmost care by the experts to polish the students’ basic knowledge. Candidates can easily understand the question pattern by referring to these solutions and prepare themselves accordingly. Below we have provided the NCERT Exercise 11.2 Class 10 Maths Solutions to help Class 10 students with their studies:

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. Also, give the justification of the construction.

Solution: The steps of construction are as follows:

Taking any point O on the given plane as centre. Draw a circle of 6 cm radius. Locate a point P,10 cm
away from O. Join OP.
Bisect OP. Let M be the midpoint of PO.
Taking M as centre and MO as radius, draw a circle.
Let this circle intersect our first circle at point Q and R.
Join PQ and PR.PQ and PR are the required tangents. The length of tangents PQ and PR are 8 cm each.

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.
Henceforth, verify the measurement by actual calculation. Also, give the justification of the construction.

Solution: The steps of construction are as follows:

Draw a circle of 4 cm radius with centre as O on the given plane.
Draw a circle of 6 cm radius taking O as its centre. Locate a point P on this circle and join OP.
Bisect OP. Let M be the midpoint of PO.
Taking M as its centre and MO as its radius draw a circle. Let it intersect the given circle at the points Q
and R.
Join PQ and PR. PQ and PR are the required tangents.

Now, PQ and PR are of length 4.47 cm each.
In ∆PQO, since PQ is tangent, ∠PQO=90o. PO=6 cm QO=4 cm Applying Pythagoras theorem in ∆PQO,
PQ2+QO2=PO2⟹PQ2+42=62⟹PQ2=20 ∴PQ=25=4.47 cm

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. Also, give the justification of the construction.

Solution: The steps of construction are as follows:

Take any point O on given plane as centre, draw a circle of 3 cm radius.
Take one of its diameters, RS, extend it on both sides. Locate two points on this diameter such that
OP=OQ=7 cm.
Bisect OP and OQ. Let T and U be the midpoints of OP and OQ respectively.
Taking T and U as its centre, with TO and UO as radius, draw two circles. These two circles will
intersect our circle at point V,W,X and Y respectively. Join PV,PW,QX and QY. These are required
tangents.

Q.4. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60o. Also, give the
justification of the construction.

Solution: Consider the above figure, PQ and PR are the tangents to the given circle.
If they are inclined at 60o, then ∠QPO=∠OPR=30o (Radius bisects the angle at P) In ∆POQ, ∠PQO=90°
Sin30°=OQOP 12=5OP OP=10 cm
Now, the steps of construction are as follows:

1. Draw a circle of 5 cm radius and with centre O.
2. Take a point Q such that OQ=10 cm.
3. Draw the perpendicular bisector of OQ to get a midpoint as P.
4. Now, draw a circle of radius OP with centre as P. Let it intersect our circle at R and S.
5. Join QR and QS. QR and QS are the required tangents.

DOWNLOAD NCERT EXERCISE 11.2 CLASS 10 MATHS SOLUTIONS

About NCERT Exercise 11.2 Class 10 Maths Solutions

The NCERT Exercise 11.2 Class 10 Maths Solutions explains how to build tangents to a circle from a point outside it. If a tangent is required at a specific location, we draw the radius through that location and construct a perpendicular to it, yielding the required tangent. If a point outside a circle exists, two tangents to the circle can be drawn. The steps for creating these tangents have been detailed in this exercise using these two principles. There are seven problems in NCERT Exercise 11.2 Class 10 Maths Solutions that are easy to solve if the student has paid attention to the basics of the chapter.

Students must learn to implement their knowledge correctly while solving the in-text questions as per the CBSE norms. Besides, while studying the chapter, students will also learn how Construction is used in real-life practises. The NCERT solutions for exercise 11.2 Class 10 Maths are presented in easy language so that the students can easily understand the concepts. The key to achieving desired grades is being patient with complex concepts and solving all the questions regularly.

NCERT Exercise 11.2 Class 10 Maths Solutions: Chapter Summary

This chapter will teach students how to divide a line segment in a particular ratio. Students can split a line segment by measuring its length and then drawing a point on it that divides it in a specific ratio. In this lesson, they will learn how to use the compass to split a line segment in a particular ratio and draw a tangent to a circle. However, they should be aware that no tangent to a circle can be generated if a point is located inside a circle. If the point is located outside the circle, there is only one tangent to a circle at this location, which is perpendicular to the radius.

There are two exercises in the chapter- Exercise 11.1 and Exercise 11.2. Both the exercises from the Constructions chapter comprise seven questions each. These questions are essential and must be practised by the students to understand geometry and its various aspects. The NCERT’s detailed solution will leave no room for further improvement as students will learn how to deal with the tricky questions during the examination.

Benefits of Practising NCERT Exercise 11.2 Class 10 Maths Solutions

We have provided you with some of the benefits of practising from the NCERT Exercise 11.2 Class 10 Maths Solutions:

1. The NCERT solutions for exercise 11.2 Class 10 Maths are based on the CBSE curriculum, making it the most reliable study material for Class 10 students.
2. The NCERT solutions are self-explanatory and are explained in very simple language, helping students understand the concepts easily.
3. The NCERT Exercise 11.2 Class 10 Maths Solutions are a complete guide for the students as they learn to tackle the difficult questions during the examination.
4. Students can adopt the same method as used in the NCERT textbooks to solve the questions as it will help them score more in the exam.
5. After practising the NCERT Exercise 11.2 Class 10 Maths Solutions, students become thorough with the chapter. They better understand the basic concepts and improve their problem-solving skills.
6. The detailed and step-wise solutions help students master the chapter, reducing their chances of making any mistake during the exam. This also boosts their confidence ahead of the exam.
7. If students are thorough with the NCERT Exercise 11.2 Class 10 Maths solutions, they can remember all the concepts at their fingertips.
8. Students also learn about the areas they are weak in and get time to work on them to reduce the chances of error.
9. Practising these solutions for NCERT Exercise 11.2 Class 10 Maths with help in securing their desired results.
10. The best part about Embibe’s NCERT Solutions is that there are no registration fees to access and download these solutions.

FAQs on NCERT Exercise 11.2 Class 10 Maths Solutions

Some of the frequently asked questions from NCERT Exercise 11.2 Class 10 Maths solutions are mentioned below:

Q.1. How many exercises are there in Chapter 11 Constructions? 
Ans. There are only two exercises in Chapter 11 Constructions for Class 10 students. Both the NCERT solutions for each exercise are available on Embibe.

Q.2. Why should students practise NCERT Solutions for Exercise 11.2 Class 10 Maths? 
Ans. Students must practise the NCERT Exercise 11.2 Class 10 Maths solutions to know the level of questions asked in the exam and understand the difficulty level. The solutions hold a piece of vital information about the chapter and must be practised before the exam to score well.

Q.3. What are the important topics covered in Chapter 11 Constructions? 
Ans. The important topics covered under Chapter 11 Constructions are the introduction to constructions, the division of a line segment, the Construction of tangents to a circle, and the summary.

Q.4. Where can I download the NCERT Exercise 11.2 Class 10 Maths Solutions? 
Ans. Students can easily access and download the NCERT Exercise 11.2 Class 10 Maths solutions on Embibe for. They can also download the solutions from the official website of NCERT.

Q.5. What are the key features of NCERT Exercise 11.2 Class 10 Maths Solutions? 
Ans. The key features of NCERT Exercise 11.2 Class 10 Maths Solutions are that the diagrams used to explain the solutions make learning more interesting for the students. The explanations are detailed but easily understandable due to the straightforward approach adopted by experts.

Now you are provided with all the necessary information regarding NCERT Class 10 Maths Solutions. We hope this detailed article helps you.

If you have any queries regarding this article on NCERT Exercise 11.2 Class 10 Maths Solutions, feel to reach out to us. We hope this detailed article helps you, ping us through the comment box below and we will get back to you as soon as possible.