Unit 9 · Circles

9.5Tangents to Circles

Quick Answer

A tangent is perpendicular to the radius at the point of tangency. Two tangent segments from an external point are congruent. A tangent-chord angle equals half the intercepted arc.

Essential Question

How does the perpendicularity of a tangent and radius lead to the two-tangent theorem and the tangent-chord angle theorem?

Learning Goals

  • 1State the Tangent-Radius Theorem.
  • 2Apply the Two-Tangent Theorem.
  • 3Apply the Tangent-Chord Angle Theorem.
  • 4Solve problems involving tangent lines.

Key Vocabulary

Tangent-Radius Theorem

A tangent to a circle is perpendicular to the radius at the point of tangency.

Two-Tangent Theorem

Two tangent segments from the same external point are congruent.

Point of tangency

The single point where a tangent line touches the circle.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.