LECTURE8-6

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Lesson 8-6:

Lesson 8-6: Segment Formulas 1 Lesson 8-6 Segment Formulas

Intersecting Chords Theorem:

Lesson 8-6: Segment Formulas 2 Intersecting Chords Theorem A B C D E Interior segments are formed by two intersecting chords. 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 a • b = c • d Theorem:

Intersecting Secants/Tangents:

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

Intersecting Secants Theorem:

Lesson 8-6: Segment Formulas 4 Intersecting Secants Theorem a • e = c • f 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.

Example::

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

Secant and Tangent Theorem::

Lesson 8-6: Segment Formulas 6 Secant and Tangent Theorem: a b c a 2 = b • d d 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

Example::

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

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