# Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius.

## The equation of a circle

$$(x-u{)}^{2}+(y-v{)}^{2}={r}^{2}$$

## The equation of a centred circle

$${x}^{2}+{y}^{2}={r}^{2}$$

## Tangency condition of a circle and a line

$${r}^{2}\left({k}^{2}+1\right)={\left(k\xb7u-v+n\right)}^{2}$$

where the equation of the tangent line is :

$$y=kx+n$$

Keywords: circle, central circle, equation of a circle, tangent to a circle