NCERT Solutions for Class 10 Maths Chapter 11: Free PDF
NCERT Solutions for Class 10 Maths Chapter 11: Chapter 11 of NCERT Class 10 Maths is called ‘Constructions’. It is a chapter that requires the students to focus on their precision in understanding and drawing geometrical figures. The Class 10 Maths Chapter 11 deals with finding the point dividing a line segment at a given ratio, constructing similar triangles, a tangent to a circle, a pair of tangents, a pair of tangents that are inclined to each other at an angle, etc.
NCERT Solutions for Class 10 Maths Chapter 11 pdf will help students to practice and prepare exercise questions from this chapter. These solutions guarantee a faster revision and save students’ time. They are prepared by subject matter experts of Embibe following the latest CBSE Syllabus. Scroll down and download the NCERT Class 10 Chapter 11 Solutions PDF from the article to prepare for your upcoming examination.
NCERT Solutions for Class 10 Maths Chapter 11: Overview
Class 10 Maths Chapter 11: Constructions (Solved Exercises)
You can access the solved exercises for Class 10 Maths Chapter 11 below. Also, you can download the CBSE Class 10 Maths Chapter 11 Solutions PDF to practice the exercises offline. You can also bookmark this page to refer to NCERT Solutions for their exam preparations. It can also help you to gain a conceptual understanding of all the topics prescribed by the CBSE board.
Q.1. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Also, give the justification of the construction. Solution: Here, we need to draw a line segment. The steps of constructions are as follows: Draw line segment AB of 7.6 cm and draw any ray AX making an acute angle with AB. Locate 13=5+8 points A1, A2,A3,A4. . . . . A13 on AX so that AA1=A1A2=A2A3=. . . =A12A13. Join BA13. Through the point A5,draw a line parallel to A13B (by making an angle equal to ∠AA13B) at A5 intersecting AB at the point C. Now C is the point dividing line segment AB of 7.6 cm in the required ratio of 5:8. We can measure the approximate lengths of AC and CB. The length of AC and CB comes to 2.9 cm and 4.7 cm respectively. Hence, the required line segment is as shown given below Justification: By the Converse of Thales theorem AA5:A5A13=AC:CB=5:
Q.2. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 23 of the corresponding sides of the first triangle. Also, give the justification of the construction.
Solution: The steps of construction are as follows: Draw a line segment AB=4 cm. Taking point A as centre draw an arc of 5 cm radius. Similarly, taking point B as its centre, draw an arc of 6cm radius. These arcs will intersect each other at point C. Now AC=5 cm and BC=6 cmand ∆ABC is the required triangle. Draw any ray AX making an acute angle with AB on opposite side of vertex C. Locate 3 points A1, A2, A3 (as 3 is greater between 2 and 3) on AX such that AA1=A1A2=A2A3. Join BA3 and draw a line through A2 parallel to BA3 to intersect AB at point B’. Draw a line through B’ parallel to the line BC to intersect AC at C’. ∆AB’C’ is the required triangle. Diagram:
NCERT Solutions for Class 10 Maths Chapter 11: Chapter Description
Class 10 Maths Chapter 11 – ‘Constructions’ is a continued discussion from Class 9 where you come across some basic constructions. In this chapter, you will learn a few more constructions using your past knowledge of the basic constructions. The two major discussions are discussed in this chapter about the division of a line segment and the construction of tangents to a circle. Besides, you will also be expected to give mathematical reasoning behind why such constructions work. Also, you will have to be good at using geometrical instruments. There are NCERT Solutions for Class 10 Maths – Chapter 11, Exercise 11.1; NCERT Solutions for Class 10 Maths – Chapter 11, Exercise 11.2; and for the rest of the exercises. Let us look at some of the real-life applications.
Real-life Examples of Constructions
The real-life examples of constructions are as follows:
Applications of Geometry in the real world include a computer-aided design for construction blueprints, the design of assembly systems in manufacturing, nanotechnology, computer graphics, visual graphs, videogame programming, and virtual-reality creation.
Geometry also plays a role in global positioning systems, cartography, astronomy, and geometry.
Before a contractor builds a structure, someone must design the building’s shape and create blueprints. A computer fitted with computer-aided design software contains the math to render the visual images of what the finished space looks like in a simulated walk-through.
Geometric constructions are used by computer and video game programmers. The way that characters move through their virtual worlds requires geometric computations to create paths around the obstacles populating the virtual world. Video game engines typically employ ray casting, which is a technique that simulates a 3-D world using a 2-D map. Using this form of geometry helps speed up processing because calculations are only done for the vertical lines on the screen. The same geometry helps a robot to see.
NASA scientists use geometric constructions to compute the journey of a vehicle sent to Mars. They use the elliptical orbits and the correct angle to enter a planet’s atmosphere and land on the surface. These are some of the many areas where constructions are used.
FAQs on NCERT Solutions for Class 10 Maths Chapter 11
Given below are a few frequently asked questions by the students:
Q1. You are given a circle of radius 3.5 cm. Calculate the distance of a point ‘P’ from the centre if a pair of tangents are drawn from the point P to the circle. Ans: ‘P’ is at a distance of 5 cm from the centre of the circle.
Q2. You are required to draw tangents at endpoints of two radii of a circle so that they are inclined at an angle of 60°. Determine the angle between the tangents. Ans: The angle between the tangents is 120°.
Q3. You are required to draw tangents at endpoints of two radii of a circle so that they are inclined at an angle of 60°. Determine the angle between the tangents. Ans:The angle between the tangents is 120°.
Q4. How many parts of a line segment are formed if it is divided in the ratio of 2:3? Ans:5 parts of a line segment are formed if it is divided in the ratio of 2:3.
Q5. Which topics are included in the NCERT Solutions for Class 10 Maths Chapter 11? Ans: The topics covered in the NCERT Solutions for Class 10 Maths Chapter 11 are as follows:
– 11.1 Introduction – 11.2 Division of a Line Segment – 11.3 Construction of Tangents to a Circle – 11.4 Summary
Q6. Can students access the NCERT Solutions for Class 10 Maths Chapter 11 in PDF format? Ans: Yes, students can access the NCERT Solutions for Class 10 Maths Chapter 11 in PDF format. Students can download the NCERT Solutions PDF from this article itself and study offline effectively.
Q7. Why should I prepare from NCERT Solutions by Embibe for my board exams? Ans: The NCERT Solutions prepared by Embibe are created by subject-matter experts to help students score maximum marks in their exams. The solutions also help students to clarify their doubts. It also helps students to gain a better understanding of all the concepts.
Q8. Can NCERT Solutions help students to score good marks in exams? Ans: Most major central and state boards in India base their curriculum on NCERT textbooks. Hence, referring to the NCERT Solutions will help students understand the concepts in a better way. This will, in turn, help students score good marks in the exams.
We have now provided you with all the necessary information regarding CBSE NCERT Solutions for Class 10 Maths Chapter 11 – Constructions. So, you can start solving the questions from this chapter. In order to understand where you are standing, you are advised to take a Mock Test on Constructions for free on Embibe. Taking mock tests on the chapter will definitely help you to secure good marks in the exam.
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