A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.
 The discus throw is a track and field event in which an athlete attempts to throw a heavy disc (called a discus) further than his or her competitors. The athlete spins counterclockwise around one and a half times through a circle, then releases the throw. When released, the discus travels on a path that is tangent to the circular spin orbit.

 Common Tangents:

Common tangents
are lines, rays or segments that are tangent
to more than one circle at the same time.
4 Common Tangents
(2 completely separate circles)

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

2 external tangents (blue)
1 internal tangent (black)
2 Common Tangents
(2 overlapping circles)
2 external tangents (blue)
0 internal tangents
1 Common Tangent
(2 internally tangent circles)
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

 If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency.

 Tangent segments to a circle from the same external point are congruent. (You may see this theorem referred to as the "hat" theorem as the circle appears to be wearing a hat.)
 With the help of the previous theorem, this theorem can be easily proven. The triangles shown at the right are congruent by Hypotenuse Leg for Right Triangles. The radii of a circle are congruent (the legs), and the triangles share a side (the hypotenuses). The triangles have right angles at A and C since a radius drawn to the point of tangency is perpendicular to the tangent. By CPCTC, the tangents are congruent.