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Daily Check

Learn how to find angle measures and segment lengths in circles, including chords, tangents, and secants. Solve equations to find unknown values.

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Daily Check

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  1. Daily Check For each circle, find the measure of x. 1. 2. x° 38° 74° 3.

  2. Warm-up Find the measures of angles 1 – 4. 52.5 4 32 2 3 105 36.5 1 105 16

  3. Math IIDay 33 (9-28-09) UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: How do we find segment lengths in circles? Standard: MM2G3.b

  4. 6.6 Segment Lengths in Circles

  5. 6.6 Segment Lengths in Circles • Find the lengths of segments of chords • Find the lengths of segments of tangents and secants

  6. Secant and Tanget 2 Secants intersecet outside Chords intersect inside

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

  8. Ex: 1 Solve for x. 9 12 6 3 x = 3 x x 2 2 x = 8 x 3 6 2 x = 1

  9. 12 2x 8 3x Ex: 2 Solve for x. 2x  3x = 12  8 6x2 = 96 x2 = 16 x = 4

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

  11. 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

  12. 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

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

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

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

  16. Homework p. 220 #2-18 (even), #28

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