Circles•Properties of Circles•Perimeter and Area

What is a Circle?A circle is defined as a plane curve formed by the set of all points which are a given fixed distance from a fixed point. Fixed distance from the centre = radius, rFixed point = centre, o

Properties of Circles1. CircumferenceThe circumference of a circle means both the boundary line and the length of the boundary line. In other words it is the perimeter of the circle, or the distance around the circle. 2.DiameterA Diameter of a circle is any straight line that joins two points on the circumference and passes through the centre. It is represented by the letter , d. *All diameters of the same circle are equal.Diameter = 2 x radius; that is, it is twice the radius.

Circle showing Circumference and Diameter

Properties of Circles Cont’d3. RadiusA radius of a circle is a straight line drawn from the centre to any point on the circumference. * All radii of the same circle are equal.Radii – plural of radius.

Circle showing Circumference, Diameter and Radius

Diagram showing radius only

Properties of Circles Cont’d4. ChordA chord of a circle is a straight line joining any two points on the circumference. Note that this line may not necessarily pass through the centre.

Diagram showing Diameter, Radius and Chord

*The Diameter of a circle is a special Chord

Properties of Circles Cont’d5. ArcAn Arc of a circle is any part of the circumference. The length of an Arc of a circle is represented by, l.

The diagram shows Arc, AB of the circle centre, O.

PROPERTIES OF Circles Cont’d6. SegmentsA segment of a circle is a plane figure bounded by a Chord and one Arc formed by the chord. The minor segment is the region bounded by the chord and the minor arc formed by the chord.The major segment is the region bounded by the chord and the

major arc formed by the chord.7.SectorsA Sector of a circle is a plane figure bounded by two radii and one Arc formed by the radii. * All Sectors of a circle with equal arc lengths or equal sector angles are equal. A minor sector has an angle at the centre of the circle of less than 180°.A major sector has an angle at the centre of the circle of more than 180°

The diagram shows a Sector and a Segment of a circle.

Properties of Circles Cont’d8. Semi – CirclesIf the Chord forms a Diameter, then the circle is divided into two equal segments and each is called a semi-circle.

Properties of Circles Cont’d9.Equal CirclesEqual Circles are circles with equal radius

If radius, r = 4cm in each circle, the circles are equal.

Concentric CirclesConcentric circles are circles which have the same centre.

Examples of Concentric circles:

•Dart Boards

•Colour Wheels

Dart Board

Colour Wheel

Examples where we can apply the Circumference of a circle:1. A jogger interested in knowing the distance around

a circular path can easily estimate its circumference.2. It can be used in Landscaping a circular area in a

yard. It is used to determine how much edging is needed for a round flower bed.

3. It is used to determine how big a label should be for a circular can or jar lid.

The Circumference and Area of a CircleThe Circumference of a Circle

Circumference = 2πr

π = 22/7 or 3.14

Area of a CircleThe area of a circle is the number of square units inside that circle.

The Area of a Circle, A = πr²

π = 22/7 or 3.14