Tangents and Circles

Tangent Definition A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.

Theorem 1 The radius of a circle is perpendicular to a tangent of that circle

Theorem 2 Tangent segments to a circle from the same external point are congruent

2 completely separate circles = 4 Common Tangents 2 external tangents (blue) 2 internal tangents (black)

2 externally tangent circles = 3 Common Tangents 2 external tangents (blue) 1 internal tangent (black)

2 overlapping circles 2 Common Tangents 2 external tangents (blue) 0 internal tangents

2 internally tangent circles One Common Tangent 1 external tangent (blue) 0 internal tangents

0 Common Tangents (2 concentric circles) Concentric circles are circles with the same center. 0 external tangents 0 internal tangents (one circle floating inside the other, without touching) 0 external tangents 0 internal tangents