Circle Equation

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

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

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.