Geometry: Tangents to a Circle

Objectives

• 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.

Vocabulary

• 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.