# Definition of circle Circumference, Area, Chord, Segment

[latexpage]

## Definition of circle

When a line AB rotate by 360 degree taking center A, thus obtained figure is called circle.

A is called center of circle. A to any point on the circle joining is called radius, a line passing through the center of the circle is called diameter of circle and its value is 2 * radius.

The ratio between circumference to diameter is always constant and denoted by $\pi$ its value is $\frac{22}{7}$ or 3.14 approximately. $\frac{pI}/D= \pi$

## Circumference of circle

so circumference of circle (p)=$\pi*D=2*\pi*r$

## Area of circle formula

Area of circle=$\pi*r^2=pi*\frac{d^2}{4}$
=$4*\pi^2*r^2/4*pi={(2*\pi*r)}^2/4*pi=(oce)^2/4pi$

We divide a circle in to many small sectors, thus the length of an arc is reached near about the length of chord.

Then merge them as below we have obtained a ractangle.

## Length of Chord Length of chord=$\frac{a^2+h^2}{2h}$
where 2a=lengh of chord
h= height of arc
$h=r+-\sqrt(r^2-a^2)$

length of arc= arc/oce=Angle in degree/360
Radion: If are is equal in length to the radious, then the angle for form are called radion.

## Segment of a circle

chord AB of a circle divides the circular region into two part, each part is called a segment of the circle. Sector of the circle– the area surrounded by an arc and the two radius joining the end point of the arc with the center is called a sector of the circle. Concentric circle– two or more circles with the given centre are called concentric circle.