Definition:Tangent to Curve/Circle

Definition

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:

Circles are said to touch one another which, meeting one another, do not cut one another.

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

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