
What is the Tangent of a Circle

A tangent has two defining properties
 A tangent touches a circle in exactly one place.
 The tangent intersects the circle's radius at a 90° angle
Since a tangent only touches the circle at exactly one and only one point, that point must be perpendicular to a radius.
To test out the interconnected relationship of these two defining traits of a tangent, try the interactive applet.
The point where the tangent and the circle intersect is called the point of tangency.
Interactive Applet (html5)
Drag around the point b, the tangent point, below to see a tangent in action.
Practice Problems
In the circles below, try to identify which segment is the tangent.

AB
is tangent to the circle since the segment touches the circle once .


VK is tangent to the circle since the segment touches the circle once.

Lengths of Tangents
