Unit 9 · Circles

9.6Secants, Tangents, and Angle Measures

Quick Answer

Angle formed by two chords inside a circle = ½(sum of intercepted arcs). Angle formed by two secants, two tangents, or a secant and tangent from an external point = ½(difference of intercepted arcs).

Essential Question

How does the location of the vertex — inside the circle, on the circle, or outside the circle — determine which arc formula to use for the angle?

Learning Goals

  • 1Apply the Chord-Chord Angle Theorem (vertex inside).
  • 2Apply the Secant-Secant Angle Theorem (vertex outside).
  • 3Apply the Secant-Tangent Angle Theorem (vertex outside).
  • 4Identify which formula to use based on vertex location.

Key Vocabulary

Chord-Chord Angle

Angle = ½(sum of intercepted arcs); vertex inside the circle.

Secant-Secant Angle

Angle = ½(difference of intercepted arcs); vertex outside 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.