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Thursday, November 14 th

Thursday, November 14 th. Warm Up. Find 1. Z 2. M<U . Homework Answers. Do you know your formulas?!!. Case I: Central Angle: Vertex is AT the center. A. . P. B. Central Angle is equal to the ______________. Arc = ___________ the inscribed angle . Angle =.

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Thursday, November 14 th

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  1. Thursday, November 14th Warm Up Find 1. Z 2. M<U

  2. Homework Answers

  3. Do you know your formulas?!!

  4. Case I:Central Angle: Vertex is ATthe center A  P B Central Angle is equal to the ______________

  5. Arc = ___________ the inscribed angle

  6. Angle =

  7. CASE IV. Vertex is OUTSIDE circle ANGLE Angle = small ARC LARGE ARC LARGE ARC LARGE ARC small ARC ANGLE small ARC ANGLE

  8. Tune: If You’re Happy and You Know It • If the vertex is ON the circle half the arc. <clap, clap> • If the vertex is INside the circle half the sum. <clap, clap> • But if the vertex is OUTside, then you’re in for a ride, cause it’s half of the difference anyway. <clap, clap>

  9. Today’s Goal Secants and tangents Side Lengths

  10. Segment Lengths in Circles • Find the lengths of segments of chords • Find the lengths of segments of tangents and secants

  11. Two chords intersect INSIDE the circle Type 1: a ab = cd d c b

  12. Solve for x. 9 6 x 2 x = 3

  13. 12 2x 8 3x Find the length of DB. x = 4 DB = 20 A D C B

  14. Find the length of each chord. D x = 8 AC = 13 DB = 14 A x - 4 x C 5 10 B

  15. Two secants intersect OUTSIDE the circle Type 2: E A B C D EA•EB = EC•ED

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

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

  18. Type 2 (with a twist): Secant and Tangent C B E A EA2= EB • EC

  19. Ex: 5 Solve for x. C B x 12 E 24 A (12 + x) 242 = 12 x = 36 576 = 144 + 12x

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

  21. Practice Problems

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