Page 1 168 MATHEMA TICS File Name : C:\Computer Station\Maths-IX\Chapter\Chap-10\Chap-10 (03-01-2006).PM65 CHAPTER 10 CIRCLES 10.1 Introduction You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of denominations 50 p, Re 1 and Rs 5, key rings, buttons of shirts, etc. (see Fig.10.1). In a clock, you might have observed that the second’s hand goes round the dial of the clock rapidly and its tip moves in a round path. This path traced by the tip of the second’s hand is called a circle. In this chapter, you will study about circles, other related terms and some properties of a circle. Fig. 10.1 Page 2 168 MATHEMA TICS File Name : C:\Computer Station\Maths-IX\Chapter\Chap-10\Chap-10 (03-01-2006).PM65 CHAPTER 10 CIRCLES 10.1 Introduction You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of denominations 50 p, Re 1 and Rs 5, key rings, buttons of shirts, etc. (see Fig.10.1). In a clock, you might have observed that the second’s hand goes round the dial of the clock rapidly and its tip moves in a round path. This path traced by the tip of the second’s hand is called a circle. In this chapter, you will study about circles, other related terms and some properties of a circle. Fig. 10.1 CIRCLES 169 File Name : C:\Computer Station\Maths-IX\Chapter\Chap-10\Chap-10 (03-01-2006).PM65 10.2 Circles and Its Related Terms: A Review Take a compass and fix a pencil in it. Put its pointed leg on a point on a sheet of a paper. Open the other leg to some distance. Keeping the pointed leg on the same point, rotate the other leg through one revolution. What is the closed figure traced by the pencil on paper? As you know, it is a circle (see Fig.10.2). How did you get a circle? You kept one point fixed (A in Fig.10.2) and drew all the points that were at a fixed distance from A. This gives us the following definition: The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle. The fixed point is called the centre of the circle and the fixed distance is called the radius of the circle. In Fig.10.3, O is the centre and the length OP is the radius of the circle. Remark : Note that the line segment joining the centre and any point on the circle is also called a radius of the circle. That is, ‘radius’ is used in two senses-in the sense of a line segment and also in the sense of its length. You are already familiar with some of the following concepts from Class VI. We are just recalling them. A circle divides the plane on which it lies into three parts. They are: (i) inside the circle, which is also called the interior of the circle; (ii) the circle and (iii) outside the circle, which is also called the exterior of the circle (see Fig.10.4). The circle and its interior make up the circular region. If you take two points P and Q on a circle, then the line segment PQ is called a chord of the circle (see Fig. 10.5). The chord, which passes through the centre of the circle, is called a diameter of the circle. As in the case of radius, the word ‘diameter’ is also used in two senses, that is, as a line segment and also as its length. Do you find any other chord of the circle longer than a diameter? No, you see that a diameter is the longest chord and all diameters have the same length, which is equal to two Fig. 10.2 Fig. 10.3 Fig. 10.4Read More

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