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NCERT Solutions for Class 10 Maths Chapter 11 Ex 11.2

 

NCERT Solutions for Class 10 Maths Chapter 11 Ex 11.2 are prepared by askIITians experts in an easy to understand way. Students can refer to these NCERT Solutions at any time and resolve their doubts regarding this exercise. Chapter 11 Constructions Ex 11.2 is based on the construction of tangents to a circle. There are 7 questions in this exercise and all are important from the exam perspective. These NCERT Solutions will be your all-time guide to help you prepare for board exams. You can also access NCERT Solutions or other exercises of Chapter 11 Constructions of Class 10 Maths on the askIITians website. 

About NCERT Class 10 Maths Chapter 11 Ex 11.2 

 

You must know that if a point lies inside a circle, there can be no tangent passing through it. However, if a point lies on the circle then there is only one tangent to the circle at this point and it is perpendicular to the radius through this point.

 

So if you want to draw a tangent to a circle follow these steps:

Step 1: Draw the radius through a point on the circle. 

Step 2: Draw a line perpendicular to this radius through this point and this will be the required tangent at the point.

 

 

Consider the image given above. We are given a circle with a centre O and a point P outside the circle. We have to construct two tangents from point P. To do that, we will follow the given steps:

 

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

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

Step 3: Join PQ and PR. PQ and PR are the required two tangents, as given in the figure above. 

Step 4: Join OQ. Then ∠ PQO is an angle in the semicircle and, therefore, ∠ PQO = 90°. 

Download Free NCERT Solutions for Class 10 Maths Chapter 11 Ex 11.2 

 

This exercise includes 7 questions where you have to draw the tangents to a circle. Let us see what kind of questions are included in this exercise and understand them at a deeper level:

 

Ex 11.2 Q1: In this question, you have to draw a circle of radius 6 cm. From a point 10 cm away from its centre, you have to construct a pair of tangents to the circle and measure their lengths. The question can be solved easily by using the steps given above. 

 

Ex 11.2 Q2: This question is based on concentric circles. In this question, you have to construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, you have to verify the measurement by actual calculation. Check our NCERT Class 10 Maths Solutions for Chapter 11 Ex 11.2 to know how to solve this question step by step. 

 

Ex 11.2 Q3: In this question, you have to draw a circle of radius 3 cm. Then, you have to take two points P and Q on one of its extended diameters, each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

 

Ex 11.2 Q4: In this question, you have to draw a pair of tangents to a circle of radius 5 cm which is inclined to each other at an angle of 60°. Can you draw a rough figure of this question just to get an idea of what this question means? If yes, then you can easily solve this question without any problem. 

 

Ex 11.2 Q5: According to this question, you have to draw a line segment AB of length 8 cm. Taking A as the centre, draw a circle of radius 4 cm and taking B as centre, you have to draw another circle of radius 3 cm. Then, you have to construct tangents to each circle from the centre of the other circle. See how to construct tangents as per this question in our NCERT Solutions for more clarity. 

 

Ex 11.2 Q6: According to this question, suppose ABC is a right triangle in which AB = 6 cm, BC = 8 cm and ∠ B = 90°. BD is perpendicular to B on AC. The circle through B, C, D is drawn. You have to construct the tangents from A to this circle.

 

Ex 11.2 Q7: This is quite an interesting question. Here, you have to draw a circle with the help of a bangle. Then, take a point outside the circle and construct the pair of tangents from this point to the circle. 

 

As you can see, all 7 questions of this exercise are easy to solve if you remember how to construct tangents to a circle. Our NCERT Solutions for Ex 11.2 of Class 10 Maths Chapter 11 Constructions will benefit you in many ways: 

  • Use our NCERT Solutions as a reference and resolve your doubts regarding the construction of tangents. 
  • You can download our NCERT Solutions in PDF form for free and study at your own pace. 
  • We encourage independent learning through these NCERT Solutions as these solutions are self-explanatory. 
  • We have included easy to understand explanations for every question. 

NCERT Class 10 Maths Chapter 11 Constructions Exercise 11.2 FAQs

 

1. Should I include explanations in every question? 

No, it is not necessary to justify every construction. You must check the marks associated with the question in the examination. If the question has a high weightage, you must justify all the constructions. 

 

2. What are some tips to make clear and correct constructions? 

You must take the measurements correctly. Use a clear, transparent ruler and a pencil with a pointy end so that you can make correct measurements. Read the question carefully and take note of everything given to you. Keep the geometry box handy as you might need a compass, protractor, ruler at any time. 

 

3. I need more help in understanding Class 10 Maths Chapter 11 Constructions. What should I do? 

askIITians Maths faculty has created NCERT Solutions for Class 10 Maths that help you understand the concepts of the chapter thoroughly. For further help, you can use our revision notes, sample papers, previous year question papers, daily practice sheets and more. You can also enrol in our online classes and learn directly from our subject experts. 


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