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Warm Up Section 3.5 Find x : 1. 2. 3.

Warm Up Section 3.5 Find x : 1. 2. 3. 4. 5. 6. x o. 104 o. 30 o. 101 o. x o. x o. 80 o. 56 o. x o. 100 o. 39 o. x o. x o. 110 o. 102 o. 110 o. 100 o.

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Warm Up Section 3.5 Find x : 1. 2. 3.

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  1. Warm Up Section 3.5 Find x: 1. 2. 3. 4. 5. 6. xo 104o 30o 101o xo xo 80o 56o xo 100o 39o xo xo 110o 102o 110o 100o

  2. Answers to Warm Up Section 3.5 Find x: 1. 2. 3. 4. 5. 6. 25o 101o 80o xo 104o 30o 101o xo xo 80o 56o xo 100o 39o xo xo 110o 102o 110o 100o 32o 104o 75o

  3. WS 9.6 • 120 2. 80 • 130 4. 30 • 4.4 6. 88 • 88 8. 48 • 9. 50 10. 25 • 11. 105 12. 75 • 42.5 14. 25 • 60 16. 122 • 17. 58

  4. Circles and Segment Lengths Section 3.5 Standard: MCC9-12.G.C.2 Essential Question: How are properties of chords, tangents and secants used to find segment lengths?

  5. The rule for finding segments formed by two chords is Part of 1st Segment Other Part of 1st Segment Part of 2nd Segment Other Part of 2nd Segment • = • Example If AB = 10, BE = 12, and BC = 5, find DB. A E 12 10 a c B 10 • x = 12 • 5 10x = 60 x = 6 5 x d b D C

  6. Segments formed by two secants Example If AB = 12, BE = 5, and BC =10, find DB. C A 5 • 12 = x • 10 60 = 10x x = 6 D E 10 12 5 x B Part Outside of 1st Segment Whole Thing Of 1st Segment Part Outside of 2nd Segment Whole Thing Of 2nd Segment • = •

  7. Segments formed by a secant and a tangent Example If AB = 16, BE = 4 find BC. A C 4 • 16 = x • x 64 = x2 8 = x E 16 x 4 B Part outside Part outside Whole thing Whole thing • = •

  8. Segments formed by two tangents Example If AB = 16, find BC A 16 • 16 = x • x 256 = x2 16 = x C x 16 Part outside Part outside Whole thing Whole thing • = • B

  9. Practice 1. 2. 14 12 6 x 9 4 x 3 6 • x = 4 • 12 6x = 48 x = 8 x • 3 = 5 • 9 3x = 45 x = 15

  10. Practice 8 3. 4. 6 x 6 8 4 4 x 4 • (4 +x ) = 6 • 14 16 + 4x= 84 4x= 68 x= 17 8 • 14 = 4 • x 112 = 4x 28 = x

  11. Practice 8 12 8 5. 6. x 12 4 x 6 4 10 6 12 – 4 = 8 12• 12 = 10 •(x+10) 144 = 10x +100 44 = 10x 4.4 = x 6 + 8 = x = 14

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