Circles: Special Segments in Circles

Properties of Tangents

Tangents have two main properties:

  1. Tangents are perpendicular to the radius at the point of tangency.
  2. Two tangents drawn from the same exterior point have the same length.

 

Property  1:
Take a look at the tangent line segment ST.

Circle U with tangent ST and radius UT
Circle with Tangent ST and Radius UT

The line segment ST is tangent at the point T.  According to the first property given, this tangent is perpendicular to radius UT.  Angle STU is a right angle. the measure of angle STU equals 90 degrees

Property 2:
Take a look at the two tangent lines draw from point Q.

Circle with tangent QA and tangent QB
Circle with Tangent QA and Tangent QB

The line segments QA and QB are tangent at the points A and B, respectively.  According to the second property given, the lengths of these segments are equals.  QA = QB.