NCERT Solutions for Class 10 Maths Chapter 11 Constructions

 

NCERT Solutions for Class 10 Maths Chapter 11 Constructions include easy explanations and stepwise answers. The main topics covered in Chapter 11 Constructions of Class 10 NCERT Maths are how to divide a line segment in a given ratio, how to construct a triangle similar to a given triangle and how to construct tangents on a circle. This chapter gives you a good understanding of how to handle geometry instruments like a compass, protractor, ruler, etc. Our NCERT Solutions for the chapter include step by step instructions about how to draw the given geometric figures. We have checked every NCERT Solution at least twice to make sure that every answer is correct and easy to understand. 

About NCERT Class 10 Maths Chapter 11 Constructions 

 

This chapter includes three types of constructions: 

• Construction 11.1: To divide a line segment in a given ratio

• Construction 11.2: To construct a triangle similar to a given triangle as per the given scale factor

• Construction 11.3: To construct the tangents to a circle from a point outside it

For every construction, you must remember the steps of construction so that you make no mistakes in your exam. Our NCERT Solutions for this chapter include all the steps with clear explanations. 

 

Steps for Construction 11.1: To divide a line segment in a given ratio

 

In this construction, you are given a line segment AB. You have to divide it in the ratio m:n, where both m and n are positive integers.

 

Suppose we want to divide AB in the ratio 3:2 (m=3, n=2)

Step 1: Draw any ray AX, making an acute angle with line segment AB.

Step 2: Locate 5 (= m + n) points A1, A2, A3, A4and A5 on AX such that AA1=A1A2=A2A3=A3A4=A4A5

Step 3: Join BA5.(A(m+n)=A5)

Step 4: Through the point A3(m=3), draw a line parallel to BA5 (by making an angle equal to ∠AA5B) at A3 intersecting AB at point C.

Then, AC : CB = 3 : 2.

 

Steps for Construction 11.2: To construct a triangle similar to a given triangle as per the given scale factor

 

Suppose we have to draw a triangle similar to ∆ABC with its sides equal to 2/3 of the corresponding sides of the given triangle ABC. (Scale factor = 2/3).

 

 

Step 1: Draw a line AX by making an acute angle with the line segment AB.

Step 2: Mark three points of equal size using a compass on the line AX. Points will be depending upon the scale factor as we have to mark the number of points that is greater in the scale factor. In the ratio of 2/3(3 > 2).

Step 3: Join BX3 and draw a line from X2 parallel to BX3 to intersect AB at P.

Step 4: Draw a line parallel to BC from point P to intersect AC at Q.

Now ∆APQ ~ ∆ABC.

 

Steps for Construction 11.3: To construct the tangents to a circle from a point outside it

You must know that a tangent is a line that intersects the circle at one point only at the outer of the circle. It is always perpendicular to the radius of the circle.

 

 

Suppose we have to construct a pair of tangents to the circle of radius 3 cm from the point which is 7 cm away from its centre and measure their lengths also.

 

Step 1: Draw a circle of radius 3 cm by taking O as the centre.

Step 2: Mark a point P outside the circle at a distance of 7 cm from the centre O. Join OP.

Step 3: Bisect the line segment OP, so that the perpendicular bisector of OP intersects it at point M.

Step 4: Now draw another circle by taking M as centre and MO as radius, which intersects the given circle at two points’ i.e. T and Tꞌ.

Step 5: Now join PT and PTꞌ which are the required tangents and measure the length of the tangents.

Download Free NCERT Solutions for Class 10 Maths Chapter 11 Constructions 

 

NCERT Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.1

Exercise 11.1 is based on constructing tangents to a circle from a point outside it and dividing a line segment in the given ratios. This exercise includes 7 questions whose stepwise solutions are provided by our Maths experts for your complete understanding of the concepts of construction. You can download the NCERT Solutions for Chapter 11 Constructions Ex 11.1 for free from our website. 

 

NCERT Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.2

The second exercise of this chapter is based on the construction of tangents to a circle from a point outside it. This exercise also includes 7 questions and is important from the exam perspective. Our stepwise solutions will help you understand this concept of construction easily. Download the solutions of this exercise in PDF form for free from our website at any time and start learning. 

 

Key features of NCERT Class 10 Maths Solutions for Chapter 11 Constructions 

• The solutions are prepared by the best Maths faculty at askIITians 
• The solutions include step by step answers for every exercise question
• You can download the solutions in PDF form and refer to them whenever you want 
• You can learn the concepts of this chapter at your own pace using these solutions 
• The solutions are based on the latest CBSE syllabus and exam pattern 

NCERT Solutions for Class 10 Maths Chapter 11 Constructions FAQs

 

1. How many questions and examples are there in the Class 10 Constructions chapter? 

Chapter 11 Constructions of Class 10 Maths includes 14 questions and 2 solved examples to help you understand three different types of constructions. 

 

2. What will you study in NCERT Class 10 Maths Chapter 11 Constructions? 

In this chapter, you will study three different types of constructions. 1) To divide a line segment in a given ratio. 2) To construct a triangle similar to a given triangle as per the given scale factor. 3) To construct the tangents to a circle from a point outside it. 

 

3. How much time will it take to complete Chapter 11 Constructions? 

Since there are just 2 exercises it would not take more than three days to complete this chapter. The first-few questions might take some time, but once you have mastered the steps of construction, it will not be difficult for you.