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.

What is true about two tangents from a common point?

Answer: They are congruent!

In the circles below, try to identify which segment is the tangent.

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

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

What must be the length of LM for this segment to be tangent line of the circle with center N?

Answer 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.

What must be the length of LM for this line to be a tangent line of the circle with center N?

Answer

What must be the length of YK for this line to be tangent to the circle with center X? Answer

(Drawing not to scale)

What is the perimeter of the triangle on the left? Note: all of the segments are tangent and intersect outside the circle. Answer 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.