DEFINITION

A circle is the locus of a point which moves in a plane, so that it its distance from a fixed point in the plane is always constant.

The fixed point is called the centre of the circle and the constant distance from the centre to any point on the circle is called its radius.

Circumference

The curve traced by the moving point is called its circumference, i.e., the equation of any circle is satisfied by co-ordinates of all points on its circumference. The equation of the circle means the equation of its circumference. It can also be defined as the set of all points lying on the circumference of the circle.

Chord and diameter

The line joining any two points on the circumference is called a chord. If any chord passes through the centre of the circle it is called the diameter of the circle.

Tangent

A line that touches the circle at only one point is a tangent to the circle

- Two tangents can be drawn to a circle from any point outside the circle and these two tangents will be equal in length.
- A perpendicular drawn from the centre of the circle to a chord bisects the chord and conversely, the perpendicular bisector of a chord passes through the centre of the circle.
- Two chords that are equal in length will be equidistant from the centre, and conversely two chords which are equidistant from the centre are equal in length.

EQUATIONS

Consider a circle having radius r. Its circumference is given by the equation :

C =

Where refers to a greek notation having value 22/7 or 3.143.

Similarly, The area of a circle with radius r is given by the formula

EXAMPLE:

A pizza pie gives us a real world example of a circle. When you make a cut from the centre of the pizza to its sides to take a slice, each side of the slice gives us the radius. If we now make a straight cut from any point on the circle, passing through its center to reach another point on the circle, it is the diameter. Many different radii and diameters pass through the centre of a circle.

EQUATIONS

The circumference of a circle having radius r is given by

C =

The area of a circle with radius r is given by the formula