Circle

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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

The equation of a centred circle

Tangency condition of a circle and a line

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

where the equation of the tangent line is :