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Xam Idea Class 10 Maths Chapter 12 Solutions: Areas Related To Circles

Xam Idea Class 10 Maths Solutions Chapter 12 ‘Areas Related to Circles’ have been prepared by Instasolv to assist you in getting your doubts sorted in the exercise questions of this chapter. In this chapter of Xam Idea solutions, you will be introduced to various new terms related to a circle such as lines intersecting the circle at different points forming components like tangents, chords, and diameter. You will also learn some important theorems about angles subtended at the centre of the circle along with the introduction to segments and secants in circles. This chapter will help you build a strong base in geometry for higher classes as well as to score full marks in the exams.

There are 52 questions arranged systematically in 6 exercises. These questions are categorized in such a manner that all the sections of the question paper in your school exams are covered thoroughly such as very short and short answer type questions, long answer type questions. The exercises, HOTS (Higher-order thinking skills) and the value-based questions will help you gain complete conceptual clarity in a question-answer format if you solve these exercises extensively using the Instasolv platform as a source of reference. Practising these questions is advised because the exercises in this chapter cover the course in a detailed fashion and are also suitable for quick revision right before your exams.

The Instasolv experts have created this set of Xam Idea Maths solutions to address your doubts simultaneously while solving the questions. Such an approach to aid you in your self-study hours will also help you boost your efficiency of studying. We aim to provide you with a one-stop solution for all your queries related to Chapter 12 ‘Area Related to Circles’ in the Xam Idea Class 10 Maths book. These solutions are really insightful and will leave you with some practical tips and tricks to approach the word problems correctly. Teaming up with our platform for your self-study will help you achieve a good rank among your batchmates.

Important Topics for Xam Idea Class 10 Maths Solutions Chapter 12: Areas Related to Circles

Introduction

  1. A circle can be defined as a group of points that are at a fixed distance, known as radius, from a fixed point which is termed as a centre.
  2. When a line and a circle lie in the same given plane then the line and circle may be non-intersecting. The line might touch the circle at one point. Such a line is termed as a tangent to the circle. When the line intersects the circle at two points, then the line is the secant for the circle.

Tangent to a Circle

  1. The tangent to a circle is the line in the same plane as the circle which intersects the circle at one point.
  2. We may also term tangents as a special case of secant, in which the two points of the chord coincide.
  3. Theorem 1: A radius drawn on the tangent at the point of contact on the circle is always perpendicular to the tangent.
  4. We can draw one and only one tangent at any given point in a circle.
  5. The line of which the radius is a part of, at the point of contact of the tangent to the circle is also referred to as the normal to the circle at that point.
  6. From an external point of the circle, there can be drawn exactly two tangents to the circle.
  7. The length of the tangent is the distance from the external point from which the tangents are drawn to the point of contact.
  8. Theorem 2: The lengths of tangents drawn on a circle from a given point lying outside the circle is equal.

Area and Circumference of a Circle

If we consider a circle of radius r, then diameter d=2r

The circumference of the circle can be calculated as circumference=π2r=πd

The area of the given circle can be calculated as, area of the circle=πr2

HereWe assume the value of pi asunless stated in the question.

Perimeter and Area of a Semicircle

The perimeter of a circle is equivalent to the half of the circumference of the circle with the given radius in addition to the length of the diameter enclosing the semi-circle. Mathematically, if the diameter is given as ‘d’ and the radius is given as ‘r’, then the

Similarly, the area of a semi-circle can be given as,

Area of a Ring

Let us assume the given ring has its outer radius as ‘R’ and the inner radius denoted as ‘r’. Then the area of the thickness of the ring can be evaluated by subtracting the area of the circle formed of radius ‘r’ from the area of the circle with radius R. Mathematically,

Area of the Sectors of Circle

A sector is formed when the ends of a given arc are joined to the centre of the circle by the radii of the circle. The minor sector is the one with the value of angle subtended at the centre less than 1800 and the major sector is the one with the value of the angle subtended by the arc at the centre is greater than 1800. Now,

Note: area of the minor sector + area of the major sector= area of the circle.

Similarly, the length of the given arc can be mathematically given as,

Area of the Segments in a Circle

The segment is a term given to the area enclosed by an arc in a circle and chord given in the circle. The area enclosing the centre of the circle is termed as the major segment while the area which excludes the centre is termed as the minor segment.

Area of the minor segment= area of the minor sector subtracted by area of the triangle subtended by the chord at the circle. Mathematically,

Exercise Discussion of  Xam Idea Class 10 Maths Solutions Chapter 12: Areas Related to Circles

Very Short Answer Type Questions

This exercise consists of 9 questions that will require minimalist answers. These questions are completely based on the formulae for the areas of a circle. You will be given with diagrams for aiding clarity in understanding the demand of the question. Some questions covered in this exercise include questions with a circle inscribed within a square or vice versa.

Short Answer Type Questions

There are 2 exercises in this section comprising 25 questions. The questions in this section are word problems based on the area of circles of which the circumference is given. In some problems, you will be required to find the area of the sectors, rates at which a circular ground can be fenced, or the diameter of a protractor with a given circumference,

Long Answer Type Questions

This exercise consists of complex problems in which you will get to evaluate the area of shaded regions in given diagrams. To solve these questions, you will require a thorough knowledge of tangents, sectors, segments, and semi-circles and important theorems.

High Order Thinking Skills (HOTS)

In this exercise, there are advanced level questions that will help you build a strong foundational base with respect to the relation of radii with circumference, segments, and sectors in a circle. You will be required to find the radii of two circles touching internally and externally both.

Value-Based Questions

The questions in this chapter are based on situational word problems such as the area occupied by tents in a camp for flood victims, the size of a circular poster prepared by a student, etc.

Why Use Xam Idea Class 10 Maths Solutions Chapter 12: Areas Related to Circles by Instasolv?

  • The Xam Idea Class 10 Maths Solutions at Instasolv are written in a simple and easy language making them inclusive in nature. 
  • We have covered each question in this chapter without compromising with the quality of answers. 
  • These answers are compliant with the latest CBSE guidelines. 
  • These solutions are interactive in nature as all the frequently occurring doubts are covered in this set after comprehensive research.