Education Technology

Tangents to a Circle

Updated on 08/18/2014

Activity Overview

Explore properties of tangent lines and how they differ from secant lines.


  • Students will define a tangent and recognize that a tangent is perpendicular to the radius of the circle at the point of tangency.
  • Students will understand that two segments tangent to a circle from a common point outside the circle are congruent.
  • Students will be able to prove that the tangent segments from an external common point are congruent.


  • secant line
  • tangent line
  • point of tangency
  • tangent segments

About the Lesson

This lesson involves students looking at tangents and their properties. As a result students will:

  • Manipulate a point on a line to visualize when it is a secant line and when it becomes a tangent line to the circle.
  • Using a constructed tangent line, describe the relationships of a tangent line to a radius at the point of tangency.
  • Using two tangent lines intersecting outside a circle, discover the relationships of tangent segments.
  • Step through and justify a proof for tangent segments.