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Segment Relationships in Circles

Segment Relationships in Circles . Geometry CP2 (Holt 12-6) K.Santos. Chord-Chord Product Theorem 12-6-1. Product of 1 chord = product of other chord a c d b Then: a(b) = c(d). Example—two chords. Find x. x 8 3 6

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Segment Relationships in Circles

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  1. Segment Relationships in Circles Geometry CP2 (Holt 12-6) K.Santos

  2. Chord-Chord Product Theorem 12-6-1 Product of 1 chord = product of other chord ac db Then: a(b) = c(d)

  3. Example—two chords Find x. x8 3 6 6x = 3(8) 6x =24 x = 4

  4. Secant-Secant Product Theorem 12-6-2 (Whole secant)(external piece) = (whole secant)(external piece) (x + w)(w) = (z + y)(y) x w y z

  5. Example—two secants Find y. 8 6 7y (Whole secant)(external piece) = (whole secant)(external piece) (6 + 8)6 = (7 + y )7 (14)6 = 49 + 7y 84 = 49 + 7y 35 = 7y y = 5

  6. Secant-Tangent Product Theorem 12-6-3 (Whole secant)(external piece) = (y + z)y= t z y

  7. Example—tangent and secant Find y. 12 8 y (whole secant) (external piece) = (8 + y)8 = 64 + 8y = 144 8y = 80 y = 10

  8. Remember an old Theorem (2 tangents) The two segments tangent to a circle from a point outside a circle are congruent. a b a = b

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