# NCERT Solutions for Class 10 Maths Chapter 11 – Constructions

Our NCERT Solutions for Class 10 Maths Chapter 11-Constructions have been prepared as per the current CBSE NCERT Class 10 Maths Book and CBSE Class 10 Maths Syllabus. Our maths experts have drafted these solutions in a crisp and concise way in a simple language to facilitate effective learning. They cover all the important concepts of the chapter. Some of them are dividing a line segment, bisecting a line segment, constructing similar triangles, and drawing tangents to a circle from a given point. This chapter comprises 2 comprehensive exercises.

Our NCERT Solutions answer all questions of both the exercises in a step by step manner. They contain full explanations and illustrative diagrams wherever necessary to help you keep your concepts clear. Our Short cut techniques, innovative study methodologies help you learn faster and score high marks in your board exams. They are fully accurate and give you a vigorous practice of all concepts covered in the chapter. This helps you become through the concepts of the chapter and build a strong conceptual base.

Our Constructions have been designed to make learning more fun, fascinating, and a much more effective process. They help you learn fast and remember more. They have been specifically designed in a manner to let you learn anywhere and anytime at your own convenience and at your own pace. They are of premium quality and are the best study resource for learning and revision purposes during your board exams.

**CBSE NCERT Class 10 Maths Chapter 11: Important Topics**

The main focus of NCERT Solutions for Class 10 Maths Chapter 11 – Constructions will be on how to draw the split of the line segment and also how to draw a triangle using a scale factor. Below is a brief overview of the chapter.

**Introduction**

In this part of the chapter, you will be learning how to draw a line segment in two different methods.

**Method 1:**This section of Class 10 Maths Constructions, discusses the bisecting of a line segment with the help of a compass. Here you will learn how to use a perpendicular bisector to split a line segment.

**Method 2**

Here you will also learn an alternative method which uses positive integers to bisect a line.

**Constructing Similar Triangle**

This section of NCERT Solutions for Class 10th Maths Chapter 11 – Constructions, will explain to you how to construct a similar type of triangles with an existing triangle. The steps for constructing similar triangles have been given below.

The above-given figure illustrates the steps of constructing a similar triangle.

**Steps of Construction**

- First, construct a triangle with ABC.
- From B, draw an acute angle of CBX with a base BC.
- Over BX, mark various points as B1, B2, B3 and B4. This could be mentioned as BB1=B1B2=B2B3=B3B4.
- Now, you have to join B4 with point c, which becomes B4C.
- Take a point as B3C’||B4C which meets BC at C’.
- Taking a point as C’ you have to draw C’A’||CA which meets AB at A’.
- Now, you can figure out that A’BC’ is the required triangle.

The above-mentioned steps are followed with scale factor > 1

**Drawing Tangents to a Circle**

This part of NCERT CBSE Class 10 Maths Chapter 11, will teach you how to draw a line which touches the circle at a particular point. It tells you that a tangent to a circle is a line which is drawn by touching at one single point to a circle. This section also teaches you about various types of tangents which are drawn to a circle. Below is a brief of the same.

**A number of tangents to a circle from a given point**

This section of CBSE NCERT Class 10 Maths Chapter 11 talks about the number of tangents that can be drawn to a circle from a given point. Here you will learn the following.

- No tangent can pass through the point given in the interior region of the circle.
- If the given point lies on the circumference of the circle, then only one tangent can be drawn through it.
- Exactly two tangents can be drawn to a circle if the point lies outside the circle.

In our NCERT Solutions for Class 10 Maths Chapter 11-Constructions, you will come to learn in detail about drawing tangents to a circle from a point outside the circle and drawing tangents to a circle from a point on the circle.

### NCERT CBSE Class 10 Maths Chapter 11 Exercise Questions

Our NCERT CBSE Class 10 Maths Chapter 11, consists of 2 exercises with a total of 14 questions. Our NCERT Solutions for Class 10 Maths Chapter 11- Constructions answer all questions of both the exercises in details with the help of illustrative diagrams wherever required. They contain step by step solutions to all questions that help you learn easily. Below is a brief overview of the exercises.

**Exercise 11.1**

This exercise of NCERT Solutions for Class 10 Maths Chapter 11-Constructions consists of 7 questions.

- Question 1 asks you to draw a line segment and divide the line into two parts with the mentioned ratios. In this question, you are also required to mention the steps and procedure by which a line is divided.
- Question 2 and question 3 are long answer questions, in which you will have to draw similar triangles to each other with the given sides.
- In question 4 you will have to draw two isosceles triangles with the given values.
- Question 5, 6 and 7 are related to the construction of a Triangle. All the three are long answer questions, in which you will have to draw triangles with the given angles and sides. For all the constructions in this exercise, you are required to give the justification for the same.

**Exercise 11.2**

This exercise of NCERT Solutions for Class 10 Maths Chapter 11, consists of 7 questions.

- Question 1 is a short answer question, in which you will have to draw a circle with a given radius and also you will have to construct a pair of tangents to the circle and measure their lengths.
- Questions 2, 3,4, 5 and 7 also cover the topic construction of a tangent to the circle.
- Question 6 is based on the right triangle. For all the constructions in this exercise, you are required to give the justification for the same.