Tangent Line
The concept of a tangent line is usually taught for the first time in geometry class. The basic definition is a line that touches a circle in exactly one point.
The example above shows a line intersecting a circle in exactly one (red) point. It is known as the point of tangency.
Other types of Lines within a Circle 
The tangent line isn't the only type of line associated with a circle. View the table below to see the names and definitions of some common lines.

A radius is a line segment connecting the center of the circle to any point on the outer edge.
All radii (the plural of radius) are equal in length. 

A diameter is a special type of chord that goes through the center of a circle.
Generally students know a dimeter better than they know a chord  its simply a line that touches two edges of the circle and goes through the center. 

A chord is a line segment in the center of a circle that touches two different edges.
If the chord also happens to go through the center of the circle, then it is called a diameter.
A diameter is the longest chord. 

A secant line is similar to a chord, except instead of being a line segment (with two ends on the edge of the circle) it is a line that extends forever.
Ever secant has a chord  its simply the part of the secant on the interior of the circle. 

Connection to Trigonometry and beyond 
The "tan", is also one of the six trigonometric functions. You can evaluate the tan of any angle using our free trig calculator or by looking up the value on our trigonometric table.
The tan is also used in many calculus applications and beyond. The concept of intersecting at exactly one point applies to all types of curves  not just circles. For a much more indepth look at Wikipedia's definition of tangent.
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