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
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