Tangents:

A tangent of a circle is a line in the same plane as the circle and the line intersects the circle at exactly one point, called the point of tangency.

Theorem:

If a line is tangent to a circle then the radius is perpendicular to the line at the point of tangency.

Corollary:

Tangents to a circle from a given point are congruent.

Theorem:

If a line is perpendicular to the radius of a circle at the radius' outer endpoint then the line is tangent to the circle.

A line that is tangent to two coplanar circle is called a common tangent.

Circles are tangent to each other when both circles are tangent to the same line at the same point