# Normal

## Normal

Synonym for perpendicular line.
A tangent is perpendicular to a radius drawn to the point of tangency of a circle. The line that contains the radius is the normal to the circle at the point of tangency.

### Example

For the point $$P\left ( x_{1}, y_{1} \right )$$ on the circle $$\left ( x-h \right )^{2}+\left ( y-k \right )^{2}=r^{2}$$, the slope of the normal is $$\frac{y-k}{x-h}$$ and its equation is$$\frac{\left ( y-y_{1} \right )}{\left ( x-x_{1} \right )}=\frac{\left ( h-y_{1} \right )}{\left ( k-x_{1} \right )}$$.