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## NCERT Solutions for Class 10 Maths Chapter 11

### 10th Maths Chapter 11 Exercise 11.1

### 10th Maths Chapter 11 Exercise 11.2

Class: 10 | Maths (English and Hindi Medium) |

Chapter 11: | Constructions |

### 10th Maths Chapter 11 Solutions

NCERT Solutions for Class 10 Maths Chapter 11 all exercises of Constructions in English and Hindi Medium are given. These NCERT Solutions are applicable for UP Board High School students also from 2022-23 onward as MP Board, UP Board has implemented NCERT Books 2022-23 for their students. Some examples of constructions are also given on this page to understand the steps of constructions. In these solutions the steps of constructions of each question of NCERT exercises are given properly.

#### Class 10 Maths Chapter 11 Solutions in Videos

#### About 10th Maths Chapter 11

Just like in Class 9, there are also the construction using a ruler and compass in class 10. In class 10 constructions we will learn to divide a line segment into given ratio, constructing a similar triangle to a given triangle and tangent to a circle from a given external point. These all constructions in class 10 requires the basic knowledge of class 9 constructions.

##### To divide a line segment in a given ratio.

In this case, a line segment is to be divided in to two part of given ratio with the help of ruler and compass. The concept of Basic Proportionality Theorem (Thales Theorem) is applied here for justification.

###### To construct a triangle similar to a given triangle as per given scale factor.

There are two cases for these type of constructions. One, the triangle to be constructed larger than the given triangle (dividing the sides into larger ratio) and two, the triangle to be constructed smaller than the given triangle (dividing the sides into smaller ratio).

Example: Construct a triangle similar to a given triangle ABC with its sides equal to 3/5 of the corresponding sides of the triangle ABC.

Steps of Constructions:

1. Let ABC be the given Δ. Draw any ray BX making an acute angle with BC on the side opposite to vertex A.

2. Locate 5 points B1, B2, B3, B4 and B5 on BX so that BB1 = B1B2 = B2B3 = B3B4 = B4B5

3. Join B5C and draw a line through B3 parallel to B5C to meet BC at C′.

4. Draw a line though C′ parallel to CA to meet AB in A′.

5. Then ΔA′BC′ is the required Triangle.

###### To construct the tangents to a circle from a point outside it.

There are also two cases depending whether the point lies on the circle or lying outside of the circle. If the point lies on the circle, we draw radius through this point and draw a line perpendicular to this radius through this point. If the point lies outside of the circle, there would be two tangents through this point.

Example: To draw tangents to a circle from a given point outside it.

Suppose C be the given circle with centre O and a point P outside it. We have to draw tangents to the circle from the point P. For that, we go through the following steps:

1. Join PO and bisect it. Let M be the midpoint of PO.

2. Taking M as centre and MO as radius, draw a circle. Let it intersect the given circle at the points Q and R.

3. Join PQ and PR. Then PQ and PR are the required two tangents.

##### Historical Facts!

The ancient Greek mathematician Euclid is the acknowledged inventor of geometry. He did this over 2300 years ago and his book ‘Element’ is still regarded as the ultimate geometry reference. In that work, he uses these construction techniques extensively and so they have become a part of the field of study in geometry. They also provide a greater insight into geometric concepts and give us tools to draw figures when direct measurement is not appropriate.

### How many questions and examples are there in class 10 chapter 11 Constructions?

There are 2 exercises in class 10 chapter 11 Constructions.

In first exercise (Ex 11.1), there are in all 7 questions.

In second exercise (Ex 11.2) also, there are in all 7 questions.

So, there are in all 14 questions in class 10 chapter 11 Constructions.

There are only 2 examples (examples 1 and 2) in class 10 chapter 11 Constructions.

### What does students study in chapter 11 Constructions of class 10 Maths?

In chapter 11 Constructions of class 10 math, students will study:

1) Construction: to divide a line segment in a given ratio.

2) How to construct a triangle similar to a given triangle as per given scale factor.

3) How to construct the tangents to a circle from a point outside it.

### How much time students need to complete chapter 11 of class 10th Maths?

Students need maximum 6 days to complete chapter 11 (Constructions) of class 10th mathematics if they are giving 2 hours per day to this chapter. Also this time depends on student’s speed, capability and many other factors.

### Is chapter 11 Constructions of class 10th mathematics difficult?

Chapter 11 (constructions) of class 10th mathematics is not very easy and not very difficult it somewhere in middle of easy and difficult. But difficulty level of anything varies from student to student. So, Chapter 11 (constructions) of class 10th mathematics is easy or not depends on students also. Some students find it difficult some find it easy or some find it in middle of easy and difficult.