Lesson 10 7 Special Segments in a Circle

Lesson 10 -7 Special Segments in a Circle Lesson 8 -6: Segment Formulas 1

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 A of the parts of the second chord. a • b=c • d Lesson 8 -6: Segment Formulas a c d E b C 2 D B

Solve for x x x 9 12 4 3 6 8 Lesson 8 -6: Segment Formulas 3

Intersecting Secants/Tangents Exterior segments are formed by two secants, or a secant and a tangent. B C B A D C E Two Secants Secant and a Tangent 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

Example: B 24 cm D m c 8 x C 10 cm A E Lesson 8 -6: Segment Formulas 6

Example: B 6 cm D A m c 2 x C 4 cm E Lesson 8 -6: Segment Formulas 7

Example: B 12 cm C 2 cm D A m c x x 3 E Lesson 8 -6: Segment Formulas 8

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. B a 2 = b • d a b c A D C d Lesson 8 -6: Segment Formulas 9

Example: B x C D 9 cm A 25 cm Lesson 8 -6: Segment Formulas 10

Solve for x x+ 2 x x+4 Lesson 8 -6: Segment Formulas 11

Solve for x 6 x 4 Lesson 8 -6: Segment Formulas 12