10 4, 10-6 circles and angles

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  • 1. CIRCLES AND ANGLES Section 10-4, 10-6 spi.3.3.A, spi.3.3.B Jim Smith JCHS
  • 2. Central Angles Are Equal To The Measure Of The Intercepted Arc Central Angles 1 63° 1 = 63°
  • 3. Inscribed Angles The Vertex Of Inscribed Angles Are On The Circle And The Sides Are Contained In Chords. 1 2 4 3
  • 4. The Measure Of An Inscribed Angle Is Equal To ½ The Measure Of The Intercepted Arc 100° 1 = ½ ( 100 ) 1 = 50° 1 2 4 3 2 = ½ (180 ) 2 = 90°
  • 5. Any Angle With It’s Vertex On The Circle Is Equal To ½ Of The Arc. 2 secants A secant and a tangent
  • 6. If The Vertex Is Somewhere Inside The Circle But Not At The Center, The Angle Is Equal To ½ The Sum Of The Arcs 8 150° 80° 8 = ½ (150 + 80) 8 = ½ ( 230 ) 8 = 115°
  • 7. If The Vertex Is Outside (A Distance Away From) The Circle, The Arc Is Equal To ½ The Difference Of The Arcs. 120° 50° 5 5 = ½ (120 - 50) 5 = ½ ( 70 ) 5 = 35°
  • 8. 1 4 = arc =1/2 arc =1/2 (sum of 2 arcs) =1/2 (difference of 2 arcs) 2 3
  • 9. D C B A F E AC is a diameter CD = 100° CB = AE BE = 50° 1 2 3 4 5 Find the Measures of the angles AF is a tangent
  • 10. D C B A F E AC is a diameter CD = 100° CB = AE BE = 50° 1 2 3 4 5 AF is a tangent 100° 80° 50° 130/2 =65 65° 65°
  • 11. D C B A F E 1 2 3 4 5 100° 80° 50° 65° 65° 1 = 80°
  • 12. D C B A F E 1 2 3 4 5 100° 80° 50° 65° 65° 2 =1/2 (65) 2 = 32 ½ °
  • 13. 3 =1/2 (180+50) 3 =1/2 (230) 3 = 115° D C B A F E 1 2 3 4 5 100° 80° 50° 65° 65°
  • 14. D C B F E 1 2 3 4 5 100° 80° 50° 65° 65° 4 =1/2 (65+50) 4 =1/2 (115) 4 = 57 ½ ° A
  • 15. 5 =1/2 (180-65) 5 =1/2 (115) 5 =57 1/2° D C B A F E 1 2 3 4 5 100° 80° 50° 65° 65°