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6.6 Finding Segment Lengths

6.6 Finding Segment Lengths. Chord-Chord Rule:. Two chords intersect INSIDE the circle. a. ab = cd. d. c. b. Example 1:. 9. 12. 6. 3. x. x. 2. 2. X = 3. X = 8. x. 3. 6. 2. X = 1. 12. 2x. 8. 3x. Example 2: Find x. 2x  3x = 12  8. 6x 2 = 96. x 2 = 16.

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6.6 Finding Segment Lengths

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  1. 6.6 Finding Segment Lengths

  2. Chord-Chord Rule: Two chords intersect INSIDE the circle a ab = cd d c b

  3. Example 1: 9 12 6 3 x x 2 2 X = 3 X = 8 x 3 6 2 X = 1

  4. 12 2x 8 3x Example 2: Find x 2x  3x = 12  8 6x2 = 96 x2 = 16 x = 4

  5. Secant-Secant Rule: OW-OW

  6. Two secants intersect OUTSIDE the circle Secant-Secant Rule: E A B C D EA•EB = EC•ED

  7. Example 3: B 13 A 7 E 4 C x D 7 (7 + 13) = 4 (4 + x) x = 31 140 = 16 + 4x 124 = 4x

  8. Example 4: B x A 5 D 8 6 C E 6 (6 + 8) = 5 (5 + x) x = 11.8 84 = 25 + 5x 59 = 5x

  9. Notice that on the tangent segment, the outside is the whole! Secant Segment External Segment Tangent Segment

  10. Secant-Tangent Rule: A secant and tangent originate from the same point OUTSIDE the circle.

  11. A secant and tangent originate from the same point OUTSIDE the circle Secant-Tangent Rule: C B E A EA2= EB • EC

  12. Example 5: C B x 12 E 24 A (12 + x) 242 = 12 x = 36 576 = 144 + 12x

  13. Example 6: 5 B E 15 C x A (5 + 15) x2 = 5 x = 10 x2 = 100

  14. What you should know by now… Given two chords Given two secants ORa tangent and a secant

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