# Definition: 3.03: Circles Touching One Another

Circles said to touch one another are any (circles) which, meeting one another, do not cut one another.

### Modern Formulation

Circles are said to touch one another when they intersect at exactly one point. There are two types of contact: 1. When a circle $$\odot AB$$ is external to another circle $$\odot EB$$, we say that the circle $$\odot AB$$ touches the circle $$\odot EB$$ externally at the point $$B$$. 1. When one circle $$\odot DC$$ is internal to another circle $$\odot EC$$, we say that the circle $$\odot DC$$ touches the circle $$\odot EC$$ internally at the point $$C$$.

When circles intersect at two points, the intersection may be referred to as a cut.

Proofs: 1 2 3 4 5
Propositions: 6 7 8 9 10 11

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### References

#### Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"

#### Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"