9.7Segment Lengths in Circles
Quick Answer
Two chords: a·b = c·d. Two secants from external point: whole × external = whole × external. Secant and tangent: tangent² = whole secant × external secant.
Essential Question
How do the three segment-length theorems for circles each arise from similar triangles, and when do you use each one?
Learning Goals
- 1Apply the Chord-Chord Product Theorem.
- 2Apply the Secant-Secant Product Theorem.
- 3Apply the Secant-Tangent Product Theorem.
- 4Identify which theorem applies based on the diagram.
Key Vocabulary
Chord-Chord Product Theorem
If two chords intersect inside a circle, then the products of their segments are equal: a·b = c·d.
Secant-Tangent Theorem
If a secant and tangent are drawn from an external point, then tangent² = (whole secant)(external segment).
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.