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9.1 Circles and Spheres

9.1 Circles and Spheres. Circle : ______________________________ ____________________________________ Given Point:______ Given distance:_______ Radius: _____________________________ ____________________________________ Chord: _____________________________

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9.1 Circles and Spheres

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  1. 9.1 Circles and Spheres

  2. Circle: ______________________________ ____________________________________ Given Point:______ Given distance:_______ Radius: _____________________________ ____________________________________ Chord: _____________________________ Secant: ____________________________ Diameter: ___________________________ Tangent: ___________________________

  3. Pt. of Tangency: _______________________ _____________________________________ Sphere: ______________________________ _____________________________________ Congruent circles: _____________________ Concentric Circles: ____________________

  4. Concentric Circles ________________________________________________________________________________________________________________________________________________________

  5. 9.2 Tangents

  6. Theorem 9.1: ________________________ ____________________________________ ____________________________________

  7. Corollary: __________________________ ___________________________________

  8. Common Tangent: __________________ __________________________________

  9. Tangent Circles: ______________________ ____________________________________

  10. P 3 Q 12 R M N S M & N are centers and P is a pt of tangency. Find: PM=____; MQ=_____; PR=____ SR=____; NS =_____; NR=_____

  11. R T O If OR=6 and TO=8 then TR=_____ If angle T= 45 degees and OT=4 then Tr=____

  12. 9.3 Arcs and Central Angles

  13. Central Angle: ____________________ _________________________________ Arc: ____________________________ A B

  14. Different Arcs: • Minor Arc: _____________________ • Major Arc: _____________________ • Semi Circle: ____________________ B O C A

  15. Minor Arc = ________________________ Major Arc = ________________________ Semicircle = _______________________ Theorem 9.3: _______________________ ___________________________________ ___________________________________

  16. Y X 30 O Z W 50 T

  17. 130 30 x x X=______ X=______

  18. A 2x-14 B 4x 2x C 3x+10 E 3x D Solve for x=______

  19. 9.4 Arcs and Chords

  20. Theorem 9.4 : ______________________ • __________________________________ • _________________________________ • _________________________________ 80 100 5 4 4 X= 80 X=___

  21. Theorem 9.5 : ____________________ • ________________________________ • _______________________________ • _______________________________

  22. Theorem 9.6 : _________________________ • _____________________________________ • _____________________________________ 5 X=___

  23. Examples: y x 6 5 y 13 x 120 Find: x=____ y=____ Find: x=____ y=____

  24. Examples: 220 y 15 x y 17 x Find: x=____ y=____ Find: x=____ y=____

  25. X 5 80 X=___ X=___

  26. 9.5 Inscribed Angles

  27. Inscribed Angle: ____________________ • ___________________________________ • __________________________________ 120 x x 120 X=_______ X=_______

  28. Corollary 1: _________________________ ___________________________________ Corollary 2: _________________________ ___________________________________ Corollary 3: _________________________ ___________________________________ ___________________________________

  29. Corollary 1Corollary 2Corollary 3

  30. Special Inscribed Angle Theorem 9.8 : _______________________ ___________________________________ ___________________________________ 80

  31. Examples: 60 x y z y x 80 x Find: x=____ y=___ 60 x=____ y=____ z=____

  32. Examples: 80 x y 60 x 140 y x Find: x=____ y=____ y=____ x=____

  33. Examples: y 20 y 20 110 x x Find: x=____ y=____ x=____ y=____

  34. D A C F B 1. 1. Given

  35. 9.6 Other Angles

  36. Inside Angle: __________________________ ______________________________________ ______________________________________ 40 x 80

  37. Outside Angle: ________________________ ______________________________________ ______________________________________

  38. 2 Tangents 2 secants Secant & Tangent

  39. Solve for x: First solve for the inside angle x 40 80

  40. Find x: 120 x

  41. Find x: x 80 20

  42. 9.7Circles and Lengths of Segments

  43. Theorem 9.11: ___________________________ ________________________________________ ________________________________________ ________________________________________ a d c b

  44. Theorem 9.12: _________________________ ______________________________________ ______________________________________ ______________________________________ d a b c

  45. Theorem 9.13: ______________________ ___________________________________ ___________________________________ b a c

  46. Solve for x: x 5 8 10

  47. Find x: 8 2 4 x

  48. Find x: x 6 4

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