The blue line in the figure above is called the "tangent to the circle c".    Another way of saying it is that the blue line is "tangential" to the circle c. (Pronounced "tan-gen-shull").

The line barely touches the circle at a single point. If the line were closer to the center of the circle, it would cut the circle in two places and would then be called a secant. In fact, you can think of the tangent as the limit case of a secant. As the secant line moves away from the center of the circle, the two points where it cuts the circle eventually merge into one and the line is then the tangent to the circle.

As can be seen in the figure above, the tangent line is always at right angles to the radius at the point of contact.

• See Tangents Through an External Point for demonstration of how to draw the two possible tangents to a circle through an external point, using only a compass and straightedge.
• See Tangents Through a Point on the Circle for demonstration of how to draw the tangent through a point on the circle , using only a compass and straightedge.

• In trigonometry, the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
• In calculus, a line is a tangent to a curve if, at the single point of contact, it has the same slope as the curve.

Other circle topics

General

• Circle definition
• Tangent
• Secant
• Chord
• Intersecting chords theorem
• Intersecting secants theorem
• Radius of a circle
• Diameter of a circle
• Area of a circle
• Concentric circles
• Annulus
• Area of an annulus
• Segment of a circle
• Area of a circle segment

Angles in a circle

• Inscribed angle
• Central angle
• Central angle theorem

Arcs

• Arc
• Arc length
• Adjacent arcs
• Major/minor arcs
• Intercepted Arc
• Sector of a circle
• Radius of an arc or segment, given height/width