A circle is a plain figure enclosed by a curved line, every point on which is equidistant from a point within, called the center.

Properties of a Circle

Radius

The distance from the center to the curve is called theradius,r, of the circle

Circumference

The boundary of a circle is called thecircumference,c.

Diameter

Any straight line passing through the center and touching the circumference at each end is called thediameter,d. Thus, d=2r

Ratio

The ratio circumference/ diameteris a constant for any circle. This constant is denoted by the Greek letterπ, c=πdorc=2πr.

Semicircle

Asemicircleis one half of a whole circle.

Quadrant

Aquadrantis one quarter of a whole circle.

Tangent

Atangentto a circle is a straight line which meets the circle at one point only and does not cut the circle when produced.ACin Figure 28.1 is a tangent to the circle since it touches the curve at pointB only. If radiusOBis drawn,angleABOis a right angle.

Sector

Thesectorof a circle is the part of a circle between radii (for example, the portionOXYof Figure 28.2 is a sector). If a sector is less than a semicircle it is called aminor sector; if greater than a semicircle it is called amajor sector

Chord

Thechordof a circle is any straight line which divides the circle into two parts and is terminated at each end by the circumference.

Segment

Segmentis the name given to the parts into which a circle is divided by a chord. If the segment is less than a semicircle it is called aminor segment If the segment is greater than a semicircle it is called amajor segment

An Arc

Anarcis a portion of the circumference of a circle. The distanceSRTin Figure 28.2 is called aminor arcand the distanceSXYTis called a major arc.

Find the circumference of a circle of a radius 20 cm

Step 1

The circumference of a circle is defined as

c=2×π×radius

Step 2

If the radius is 20 cm and π = 3.142, applying the formula, then the circumference is

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