Lesson 10-7: Segment Formulas

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 B C D E a d b c a • b = c • d Lesson 10-7: Segment Formulas

Intersecting Secants/Tangents Exterior segments are formed by two secants, or a secant and a tangent. D B C A D B A C E Secant and a Tangent Two Secants Lesson 10-7: Segment Formulas

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 10-7: Segment Formulas

Lesson 10-7: Segment Formulas Example: AB  AC = AD  AE D B A C E 4 cm 4  10 = 2  (2+x) 6 cm 2 cm 40 = 4 + 2x x 36 = 2x X = 18 cm Lesson 10-7: Segment Formulas

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. D B C A a2 = b • d a b c d Lesson 10-7: Segment Formulas

Lesson 10-7: Segment Formulas Example: D B C A x 9 cm 25 cm Lesson 10-7: Segment Formulas