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Chord AB is 18. The radius of Circle Q is 15. How far is chord AB from the center of the circle?

Chord AB is 18. The radius of Circle Q is 15. How far is chord AB from the center of the circle?. 9. A. B. x. 15. Q. (family!) 12. Chord AB is 40, and is 15 units from the center of the circle. Find the radius of Circle Q. 20. A. B. 15. x. Q. (family!) 25.

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Chord AB is 18. The radius of Circle Q is 15. How far is chord AB from the center of the circle?

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  1. Chord AB is 18. The radius of Circle Q is 15. How far is chord AB from the center of the circle? 9 A B x 15 Q (family!) 12

  2. Chord AB is 40, and is 15 units from the center of the circle. Find the radius of Circle Q. 20 A B 15 x Q (family!) 25

  3. Chord AB is 16 units from the center of circle Q. The radius of circle Q is 34. Find the length of chord AB. A x B 16 34 Q (family!) x = 30 AB = 60

  4. AC = EF AB = 3x + 1 QC = 4x QF = 2x + 6 Find the radius of circle Q. A 5 C B 12 4x x 2x + 6 D Q Because AC = EF, AB = DE. So, they are equidistant from the center 4x = 2x + 6 2x = 6 x = 3 QC = 4(3) = 12 AB = 3(3) + 1 = 10 F E (Family!) 13

  5. B = 20˚ = 64˚ Find m<AEB A E P x = 20 + 64 2 x = 42˚ C D

  6. B < AEC = 142˚ = 100˚ Find m A E P 142 = 100 + x 2 284 = 100 + x x = 184˚ C D

  7. B m<AEB = 47˚ = 80˚ Find A E (x = arc AB) 47 = 80 + x 2 94 = 80 + x x = 14˚ P C D Arc DB = 180 – 14 = 166˚ (180 b/c AD is a diameter)

  8. = 95˚ Find m<B B x = 95 2 x = 47.5˚ P C D

  9. m<B = 33˚ Find B (x = arc CD) 33 = x 2 x = 66˚ P C Arcs BC and BD are congruent b/c the chords are congruent, so 360 – 66 = 294 294/2 = 147˚ D

  10. m<B = 38˚ = 165˚ Find <C B (x = arc CD) 38 = x 2 x = 76˚ P Tangent! C D Arc BC = 360 – (76 +165) = 119 <C = 119 = 59.5˚ 2

  11. B A C P = 130˚ = 60˚ Find m<B x = 130 - 60 2 x = 35˚ D

  12. B A C <B = 29˚ = 54˚ Find P D 29 = x - 54 2 58 = x – 54 x = 112˚ E

  13. A B C P = 200˚ Find <B D x = 200 – 160 2 x = 20˚ = 360 – 200 = 160

  14. <B = 85˚ Find A C B P x = arc ACD Arc AD = 360 – x 85 = x – (360 – x) 2 170 = x – 360 + x 530 = 2x x = 265˚ D

  15. Find B = 120 = 360 – 120 = 240˚ C 120˚ P D

  16. C D The radii are 20 and 35; PB = 39. Find CD 20 20 15 B 39 P x2 + 152 = 392 x = 36 (5, 12, 13 family)

  17. C 40 D The radii are 11 and 20; CD = 40. Find PB 11 11 9 B P 402 + 92 = x2 x = 41 (BTW, also a family)

  18. Circles B, C and P are tangent BC = 19 CP = 22 BP = 17 Find the radius of circle B B x 19 - x x C 19 - x 17 - x 17 - x P 17 – x + 19 – x = 22 -2x + 36 = 22 -2x = -14 x = 7

  19. Circles B, C and P are tangent BC = 9 CP = 20 BP = 7 Find the radius of circle P 7 - x B 20 - x 7 - x C 20 - x x x P 7 – x + 20 – x = 9 -2x + 27 = 9 -2x = -18 x = 9

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