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RS Aggarwal Class 10 Chapter 9 Solutions (Constructions)

RS Aggarwal Class 10 Maths Solutions for Chapter 9 ‘Constructions’ are important for you to get the highest marks in your Class 10 board examination. In this chapter of RS Aggarwal Class 10 Maths Solutions, there are 20 problems divided into 2 exercises. The solutions are well structured to improve your concept-based knowledge. You will get an idea of writing steps of constructions based on the division of a line segment and construction of similar triangles. 

This chapter will also help you to understand some important constructions of tangents to a circle alongside the principle of calculation of the number of tangents to a circle. The exercise questions of the chapter enable you to create similar triangles when the angles of a triangle are given along with the ratio of the lengths of the two triangles. You will also be constructing different types of triangles such as isosceles, scalene and right angles triangles. 

RS Aggarwal Solutions for Class 10 Maths Chapter 9 ‘Constructions’ by our subject matter experts will help you understand every step of constructions given in the questions. All the questions are based on CBSE Class 10 Maths syllabus. Use our solutions as a guide and achieve better marks in your board exams. 

Important Topics for RS Aggarwal Solutions for Class 10 Maths Chapter 9 –Constructions

  • Bisecting a Line Segment 
    • Step 1: With a radius of more than half the length of the line segment, draw concentric arcs on each end of the line segment so that it intersects on each side of the segment. 
    • Step 2: Join the intersection points. The line segment is divided in half by the line segment joining the intersection points.

 

PQ is the perpendicular bisector of AB

  • Dividing a Line Segment 

For a given line segment AB, divide it by the ratio m: n, where m and n are natural numbers. Suppose we want to divide AB in a ratio of 3: 2 (m = 3, n = 2). 

    • Step 1: Draw any radius AX, making an acute angle with a line segment AB.
    • Step 2: Find 5 (= m + n) points A1, A2, A3, A4 and A5 on AX so that AA1 = A1A2 = A2A3 = A3A4 = A4A5
    • Step 3: Join BA5. (A (m + n) = A5)
    • Step 4: Crosspoint A3 (m = 3) draw a line parallel to BA5 (making the angle equal to ∠AA5B) at point A3 intersecting AB at point C. Then, AC: CB = 3: 2.

  • Construction of Similar Triangles
    • By using scale factor: Suppose you want to construct a triangle with sides are 3/4 times along with the corresponding sides of a given triangle:

    • Step 1: Draw any ray BX with side bc (opposite side of vertex A) at an acute angle.
    • Step 2: Mark 4 consecutive distances (the required ratio is 4) on the BX as shown.
    • Step 3: Join B4C as shown in the figure.
    • Step 4: Draw B3 parallel to B4C for the intersection at BC at ‘C’. 
    • Step 5: Draw a “C” line parallel to “AC ‘ and intersect AB at “A” which is a required triangle. The same procedure can be followed when the scale factor> 1.
  • Tangents to a Circle
    • A tangent to a circle is a line that touches a circle at exactly one point. For each point of the circle, a unique tangent crosses it.

PQ is the tangent touching the circle at A

  • The Number of Tangents to a Circle from a given point
  • If the factor in an interior vicinity of the circle, any line form that factor will be a secant. So, in this case, there’s no tangent to the circle.

     AB is a secant drawn from the point S

  • In a situation where the point lies on the circle, there is only 1 tangent to a circle.

         PQ is the tangent touching the circle at A

  • In a situation where the point lies outside of the circle, there are two tangents to a circle.

                      PT1 and PT2 are tangents touching the circle at T1 and T2

  • This chapter is going to help you in construction of tangents to a circle from a point outside the circle

  • Steps to be followed while constructing the tangents to a circle from a point outside it: Let us Consider a circle having a centre” O” and “P” be the exterior point from where you will draw tangents.
    • 1st step: Join the PO and bisect it. “M”= midpoint of “PO”.
    • 2nd step: Taking M as the centre and MO (or MP) as radius, draw a circle. Let it intersect the given circle at the points Q and R.
    • 3rd step:  now join PQ and PR
    • 4th step:  As a result, “PQ” and “PR” are the required tangents to the circle.

Exercise Discussion for RS Aggarwal Solutions for Class 10 Maths Chapter 9 –Constructions

Exercise 9A 

It has 10 questions based on the division of a line section in a given ratio and creation of a triangle according to the given scale factor. You will be constructing different types of triangles as well in the exercise. 

Exercise 9B 

It has 10 questions that mainly focus on vital problems based on the construction of tangent to a circle. This exercise will ask you to perform steps of constructions by using simple approaches with the assist of several diagrams. You will get a chance to construct: a tangent to a circle at a given point on the circle also a tangent to a circle at a point over it irrespective of the centre point and more.

Why Use RS Aggarwal Class 10 Maths Solutions for Chapter 9 – Constructions by Instasolv?

  • The RS Aggarwal Solutions of Class 10 Chapter 9 not only strengthen your foundation in the subject but also give you the ability to easily answer questions of all types. 
  • These solutions will help you in solving and clarifying your doubts about the questions in the exercises. Though the questions seem very easy, they need good preparation.
  • The solutions will help you to revise the whole chapter in less time. These solutions can help you with the board exams as well as daily homework. 
  • These solutions are prepared to provide you with an effortless and complete understanding of every concept and theorems of the chapter. 
  • Practising the questions of the chapter will improve your level to solve different problems and you will also learn time management while solving problems.