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Equations of Circle

What is a circle?

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 the radius, r, of the circle

  • Circumference

The boundary of a circle is called the circumference, c.

  • Diameter

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

  • Ratio

The ratio circumference/ diameter is a constant for any circle. This constant is denoted by the Greek letter π, c = π d or c = 2π r.

  • Semicircle

A semicircle is one half of a whole circle.

  • Quadrant

A quadrant is one quarter of a whole circle.

  • Tangent

logarithms example

A tangent to a circle is a straight line which meets the circle at one point only and does not cut the circle when produced. AC in Figure 28.1 is a tangent to the circle since it touches the curve at point B only. If radius OB is drawn, angle ABO is a right angle.

  • Sector

logarithms example

The sector of a circle is the part of a circle between radii (for example, the portion OXY of Figure 28.2 is a sector). If a sector is less than a semicircle it is called a minor sector; if greater than a semicircle it is called a major sector

  • Chord

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

  • Segment

Segment is 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 a minor segment If the segment is greater than a semicircle it is called a major segment

  • An Arc

An arc is a portion of the circumference of a circle. The distance SRT in Figure 28.2 is called a minor arc and the distance SXYT is 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

2πr = 2π (20.0)

=  2 x 3.142 x 20

= 125.68 cm



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