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What is the Tangent of a Circle

applet

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

picture of tangent of circle
non example of tangent of a circle
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! (Read more about tangents from a common point)

Two Tanents from A common point
Practice Problems


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

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Identify the tangent to the circle
Answer

Lengths of Tangents

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

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

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

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(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