# NCERT Exemplar Class 10 Maths Chapter 10 Solutions: Constructions

NCERT Exemplar Class 10 Maths Solutions Chapter 10 ‘Constructions’ has been prepared to guide you in the CBSE board exams by providing a reliable source of reference for the exemplar exercises. In the NCERT Exemplar Class 10 Maths Chapter 10, you will learn how to divide a line segment in a given ratio and construction of a triangle similar to another triangle on a given scale. Also, you will learn how to construct two tangents on a circle from an external point in this chapter.

In this chapter, there are a total of 21 NCERT Exemplar problems categorized in 4 exercises according to the level of difficulty. There are questions where you will have to find out the length of tangents or angles in certain cases. You will also have to state if a given sentence is right or wrong in the exemplar questions. All the topics have been covered thoroughly in these exercises.

We have provided topic-wise coverage of the chapter in the question-answer format at Instasolv through our NCERT Exemplar solutions for Class 10 Maths Chapter 10. You will get reliable assistance from these solutions. To amplify your marks exponentially, you should solve all the exemplar questions after practising the NCERT topics related to Constructions.

## Important Topics for NCERT Exemplar Class 10 Maths Solutions Chapter 10: Constructions

**To Divide a Line Segment in a Given Ratio**

If we assume a line segment AB of a certain length and decide to divide it in a given ratio, say m:n, such that m and n are positive integers, then we can follow either of the two methods mentioned below:

Method 1

Step 1: Draw a ray from one of the end-points of the line segment AX, making an acute angle with the same.

Step 2: Now find the sum of m and n. Mark m+n sections on AX which are equidistantly using a compass.

Step 3: You can name these points as A_{1}, A_{2},… ,A_{m+n}.

Step 4: Join A_{m+n}to B.

Step 5: Now, draw a line parallel to A_{m+n}B passing through Amintersecting AB at C. You will find that AC: CB = m:n.

Method 2

Step 1: Draw a ray from one of the end-points of the line segment AX, making an acute angle with the same.

Step 2: Draw another ray from point B, BY making the angle ∠YBA = ∠XAB.

Step 3: Mark equidistant points on AX, which are m in number. Similarly, mark points on BY which are n in number.

Step 4: Join the line segment A_{m}B_{n}. This line segment will intersect AB at C such that AC: CB= m:n.

**Construction of Similar Triangles**

You should understand that the scale factor refers to the ratio of the corresponding sides of the reference triangle.

To draw a similar triangle, you can draw one side parallel to its corresponding side, by dividing one of its adjacent sides in the given scale factor using the methods above.

**Construction of Tangents to a Circle with Centre O from an External Point P**

Step 1: Bisect the line PO at M.

Step 2: With M as the centre, draw a circle intersecting the given circle at M and N.

Step 3: Join PM and PN to get the desired tangents.

**Exercise Discussion of NCERT Exemplar Class 10 Maths Solutions Chapter 10: Constructions**

- To solve the exercise questions of 10.1, you will need in-depth knowledge about the points that should be joined to divide a line segment in a certain ratio. All the questions in this exercise are multiple-choice questions.
- The questions in exercise 10.2 are reasoning-based, true or false statements. All the above-stated topics have been covered in this exercise. You should know the importance of acute angles in construction to be able to solve this exercise.
- You can solve the exemplar questions from exercise 10.3 easily by following the steps given in the solutions by Instasolv. This exercise will fetch you confirmed marks with the least scope of committing mistakes.
- In exercise 10.4, you will get to construct more complicated questions using all the knowledge you have gained extensively.

**Why Use NCERT Exemplar Class 10 Maths Solutions Chapter 10: Constructions by Instasolv**

- Our NCERT Class 10 Exemplar solutions for Maths Chapter 10 are an excellent source of reference for revision before your CBSE exams.
- The Instasolv solutions include solved CBSE exam questions as well that were taken from the Exemplar exercises of this chapter.
- You will get answers to each question without a compromise in the quality of the solutions at Instasolv.
- To score well in the exam, you should only look up to NCERT Solutions and NCERT Exemplar Class 10 Maths Solutions as they are self-sufficient and covers the entire syllabus of CBSE.