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BASIC GEOMETRICAL CONCEPTS CIRCLE Developed by: NARESH TANGRI KAVITA KATARIA MUKESH MITTAL

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CONTENTS CIRCLE CENTRE RADIUS DIAMETER CIRCUMFERENCE CHORD ARC SECTOR CENTRAL ANGLE AREA OF A CIRCLE CLICK ON EACH CONTENT POINT TO LEARN ABOUT IT OR CLICK ON NEXT NEXT

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OBJECTIVES After interacting with this software the learner will be able to : Define a circle. Draw a circle. Define the diameter of the circle Define the radius of the circle Define and calculate the circumference of the circle. Define chord,sector,arc,and central angle of the circle. Calculate the radius and the diameter of the circle. Define and calculate the area of the circle. BACK NEXT CONTENTS

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TARGET GROUP AGE GROUP 13 TO 15 YEARS CLASSES VII-IX BACKNEXTCONTENTS

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C DRAWING A CIRCLE BACK TO CONTENTSNEXT

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CIRCLE CIRCLE is the locus of a point which moves in a plane so that its distance from a fixed point remains constant. BACK TO CONTENTSNEXT

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EXAMPLES OF CIRCLE IN DAILY LIFE NEXT BACK

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RADIUS OF A CIRCLE Radius of a circle is a line joining centre of the circle to any point on the circle. C A B D E F BACK TO CONTENTSNEXT

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A chord is any straight-line segment that is intercepted by the circle. CHORD OF A CIRCLE C AB BACK TO CONTENTSNEXT

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c DRAWING A CIRCLE BACKNEXT CONTENTS

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DIAMETER OF A CIRCLE Any Line that passes through the centre and is terminated by the circle is called DIAMETER of the circle. C A B BACK TO CONTENTSNEXT

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CENTRE OF THE CIRCLE ` The fixed point inside the circle which is at equal distance from every point on the circle is called CENTRE of the circle. C BACK TO CONTENTS NEXT

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SECTOR OF THE CIRCLE The part of circle bounded between two radii of a circle is called the SECTOR of the circle. BACK TO CONTENTS NEXT A B C

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ARC OF A CIRCLE The part of the circumference of the circle is called an arc of the circle. B A BACK TO CONTENTSNEXT

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CENTRAL ANGLE C A B The angle subtended by an arc of a circle at it’s centre is called central angle. BACK TO CONTENTSNEXT

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CIRCUMFERENCE OF A CIRCLE AB NEXT BACK

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AB BACK TO CONTENTS CIRCUMFERENCE OF A CIRCLE NEXT

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CIRCUMFERENCE OF A CIRCLE AB BACK NEXT

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лr r AREA OF A CIRCLE. Area of Circle= πr 2 BACK TO CONTENTS NEXT

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CIRCUMFRENCE OF A CIRCLE Π CIRCUMFRENCE DIAMETER CONSTANT C D (CONSTANT) Where Π 22 7 3.14 C=Π D = 2Πr BACK TO CONTENTSNEXT

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EXERCISE 3 Circumference of a circle whose radius is 3.5 cm will be: (a)11cm (b)22cm. (c)33cm. (d)44cm. Click here for answer

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Example 1: Find the circumference of a circle whose radius is 14 cm. Solution: Radius =14cm. Circumference= 2 π r = 2 x 22/7x14=88cms. ILLUSTRATIONS BACK NEXT

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EXERCISE 1 CHOOSE THE CORRECT ANSWER If radius or circle is doubled its circumference will (a) Remain same. (b)Become double (c) Become half (d) None of these For correct answer click hereFor correct answer click here.

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Example 2 :Find the distance covered by a bicycle in 100 revolutions, if the radius of its wheel is 70 cm. Solution: Given : Radius of the wheel=7 cm. Distance covered in one revolution of the wheel =circumference of the wheel =2πr Distance covered in 100 revolutions = 440 x 100 2x22/7x70=440cm. =44000cm =440 meter BACK NEXT

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EXERCISE 2 If radius of a circle is halved its area will (a)Become double of itself (b)Become half of itself (c)Become one fourth of itself. (d)Become four times of itself. For correct answer click here.

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EXERCISE 4 The area of a circle whose radius 10.5cmis (a)364.5cm 2 (b)346.5cm 2 (c)355.5cm 2 (d)336.5cm 2 Click here to see answerClick here to see answer.

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EXERCISE 1.Find the radius of a circle whose circumference is220cm. 2.Find the circumference of a circle whose diameter is 21cm. 3.Determine the area of a circle whose radius is 14cm. 4.Determine the area swept by minute hand of a clock in one hour,if the length of minute is 7cm. ANS.(1)35cm. (2)63cm.(3)616cm 2. (4)154cm 2. BACKNEXT

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EXAMPLE :3 A horse is tied to a rope of 42 cm of length at the center of a rectangular grassy plot. How much area will it graze in one complete round trip. Solution: Radius of circular path = 42 cm Area grazed by the horse = πr 2 =22/7x42x42= 6544 cm 2 BACK NEXT

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ANSWERS 1.(a) 2(c) 3(b) 4(b) BACK TO EXERCISE1 BACK TO EXERCISE 2 BACK TO EXERCISE 3 BACK TO EXERCISE 4 NEXT

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ACKNOWLEDGEMENT We are sincerely thankful to SH. V.K.SODHI Sh.NARESH KAPOOR Mrs.RENU

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