#### What is the Tangent of a Circle?

Answer: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.

**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

For segment LM to be a tangent it intersect the radius MN at 90°. Therefore triangle LMN would have to be a right triangle and the Pythagorean theorem provides the necessary length for LM to be a tangent.

Each side length that you know (5,3,4) is equal to the side lengths in red because they are tangent from a common point