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Circle Segment Relationships Theorems in Geometry

Explore chord-chord, secant-secant, and secant-tangent product theorems for intersecting segments within and outside a circle. Understand how to calculate segment lengths based on theorem requirements.

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Circle Segment Relationships Theorems in Geometry

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  1. Chord-Chord Product Theorem Module 19: Lesson 4Segment Relationships in Circles If 2 chords intersect inside a circle, then the products of the lengths of the segments of the chords are equal. B A AC · CE = BC · DC C See example 1 page 1043 E D

  2. Secant-Secant Product Theorem If 2 secants intersect in the exterior of a circle, then the products of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. BC · AC = CE · CD A B C D E See example 3 page 1045

  3. Secant-Tangent Product Theorem If a secant and a tangent intersect in the exterior of a circle, then the product of the lengths of one secant segment and its external segment equals the length of the tangent segment squared. A See example 4 page 1046 B C D

  4. Homework pages 1049-1053 #’s 5-20 (all)

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