MATHEMATICS PROJECT WORK :
MATHEMATICS PROJECT WORK TOPIC- CIRCLES
GUIDED BY:P.JAYADURGA ACKNOWLEDGEMENT :
ACKNOWLEDGEMENT I would like to express my special thanks of gratitude to my teacher P.JAYADURGA who gave me the golden opportunity to do this wonderful project on the topic CIRCLES, which also helped me in doing a lot of Research and i came to know about so many new things. I would also like to thank my parents who helped me a lot in finishing this project within the limited time.
I am making this project not only for marks but to also increase my knowledge .
THANKS AGAIN TO ALL WHO HELPED ME. CONTENTS :
CONTENTS INTRODUCTION
PARTS OF CIRCLE
TANGENT TO A CIRCLE
CIRCUMFERENCE OF CIRCLE OF CIRCLE
AREA OF
CIRCLE
AREA OF LENGTH OF AN ARC OF A SECTOR OF A CIRCLE
OTHERS CIRCLE :
CIRCLE A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point .
Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. CIRCULAR REGION :
CIRCULAR REGION A CIRCLE DIVIDES THE PLANE INTO THREE PARTS
INTERIOR OF CIRCLE
THE CIRCLE
EXTERIOR OF CIRCLE PARTS OF CIRCLE :
PARTS OF CIRCLE Centre
Radius
Diameter
Circumference
Chord Tangent
Secant
Sector
Segment
Arc
Semi-circle CENTRE :
CENTRE A fixed point inside the circle which is equidistance from all the points of circle is called a CENTRE.
Here point A is the centre RADIUS :
RADIUS The radius of a circle is the distance from the center of a circle to any point on the circle.
The plural of radius is radii. DIAMETER :
DIAMETER The distance across a circle through the center is called the diameter.
It is the twice of the length of the radius. CIRCUMFERENCE :
CIRCUMFERENCE The circumference of a circle is the boundary line or the perimeter of the circle.. CHORD :
CHORD The chord is a straight line joining two points on the circumference points of a circle. The diameter is a special kind of the chord passing through the center. TANGENT :
TANGENT A tangent is a straight line which touches the circle. It does not cut the circumference. The point at which it touches, is called the point of contact. SECANT :
SECANT A secant is a straight line that intersects a curve at two points. SECTOR :
SECTOR A circular sector or circle sector, is the portion of a circle enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. SEGMENT :
SEGMENT A circular segment is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. ARC :
ARC An arc is a part of the circumference between two points or a continuous piece of a circle. The shorter arc between and is called the minor arc . The longer arc between and is called the major arc . SEMI-CIRCLE :
SEMI-CIRCLE A semi-circle is an arc which is half of the circumference . TANGENT TO A CIRCLE :
TANGENT TO A CIRCLE Theorem 1
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Theorem 2
The lengths of a tangents drawn from an external point to a point to a circle are equal. CIRCUMFERENCE OF CIRCLE OF CIRCLE :
CIRCUMFERENCE OF CIRCLE OF CIRCLE The circumference of a circle is the length around it. The circumference of a circle can be calculated from its diameter using the formula:
Or, substituting the radius for the diameter: AREA OF CIRCLE :
AREA OF CIRCLE The area enclosed by a circle is π multiplied by the radius squared: AREA OF SECTOR :
AREA OF SECTOR . AREA OF LENGTH OF AN ARC OF A SECTOR OF A CIRCLE :
AREA OF LENGTH OF AN ARC OF A SECTOR OF A CIRCLE We need to find the fraction of the circle that the sector angle represents, and then find that fraction of the circumference. CIRCLES IN DAILY LIFE :
CIRCLES IN DAILY LIFE Slide 24:
THE END