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Segment Formulas and Theorems for Intersecting Chords and Secants/Tangents

Learn about the intersection of chords, secants, and tangents in a circle and how their lengths relate according to various theorems. Practice examples included.

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Segment Formulas and Theorems for Intersecting Chords and Secants/Tangents

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  1. Learning Target 9 Segment Formulas Lesson 8-6: Segment Formulas

  2. A D E B C Intersecting Chords Theorem Interior segments are formed by two intersecting chords. Theorem: If two chords intersect within a circle, then the product of the lengths of the parts of one chord is equal to the product of the lengths of the parts of the second chord. a d b c a • b = c • d Lesson 8-6: Segment Formulas

  3. B A B C D A D C E Intersecting Secants/Tangents Exterior segments are formed by two secants, or a secant and a tangent. Secant and a Tangent Two Secants Lesson 8-6: Segment Formulas

  4. Intersecting Secants Theorem If two secant segments are drawn to a circle from an external point, then the products of the lengths of the secant and their exterior parts are equal. a • e = c • f Lesson 8-6: Segment Formulas

  5. A B C D E Example: AB AC = AD  AE 4 cm 4  10 = 2  (2+x) 6 cm 2 cm 40 = 4 + 2x x 36 = 2x X = 18 cm Lesson 8-6: Segment Formulas

  6. B A D C Secant and Tangent Theorem: The square of the length of the tangent equals the product of the length of the secant and its exterior segment. a2 = b • d a b c d Lesson 8-6: Segment Formulas

  7. B A D C Example: x 9 cm 25 cm Lesson 8-6: Segment Formulas

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