# Definition:Tangent/Geometry

## Definition

### Tangent Line

In the words of Euclid:

*A straight line is said to***touch a circle**which, meeting the circle and being produced, does not cut the circle.

(*The Elements*: Book $\text{III}$: Definition $2$)

In the above diagram, the line is **tangent** to the circle at the point $C$.

### Tangent Circles

In the words of Euclid:

(*The Elements*: Book $\text{III}$: Definition $3$)

In the above diagram, the two circles are **tangent** to each other at the point $C$.