When you have a straight line and a circle, there are three possibilities: The line does not enter or touch the circle. The line cut the circle in two points. The line touch the circle at one point only.

The image describes the three possible relationships between a straight line and a circle, and introduces a key theorem about tangents.

Here are the three possibilities for a straight line and a circle:

• No Intersection: The line does not touch the circle at any point. This line is outside the circle.
• Secant Line: The line cuts the circle in two distinct points. This line is called a secant.
• Tangent Line: The line touches the circle at exactly one point. This line is called a tangent. The point where it touches is called the point of tangency.

The theorem mentioned at the bottom of the page is a fundamental property of tangents:

• Theorem: A tangent to a circle is perpendicular to the radius drawn to the point of tangency.