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10-6 Circles and Arcs

10-6 Circles and Arcs. Learning Goals 1. To find the measures of central angles and arcs. 2. To calculate the circumference and arc length. What is the measure of the angle all the way around B?. B. C. What is the measure of the angle all the way around B? 360˚. B. C.

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10-6 Circles and Arcs

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  1. 10-6Circles and Arcs

  2. Learning Goals1. To find the measures of central angles and arcs.2. To calculate the circumference and arc length.

  3. What is the measure of the angle all the way around B? B C

  4. What is the measure of the angle all the way around B? 360˚ B C

  5. If m ABC = 60°, A B C

  6. If m ABC = 60°,then the m ABC = ? A B C

  7. If m ABC = 60°,then the m ABC = 300°. A B C

  8. Central AngleAn angle whose vertex is at the center of a circle. Central Angle

  9. ArcsThe sections of the circle separated by the central angles. arcs

  10. Arcs are measured by their corresponding central angle. m ABC = 80 m AC = ? A 80° B C D

  11. Arcs are measured by their corresponding central angle. m ABC = 80 m AC = 80 A 80° B C D

  12. Arcs are measured by their corresponding central angle. m ABC = 80 m AC = 80 m ADC = ? A 80° B C D

  13. Arcs are measured by their corresponding central angle. m ABC = 80 m AC = 80 m ADC = 280 A 80° B C D

  14. Minor arc: less than 180° and 2 letters are used for the name.

  15. Major arc: greater than 180° and 3 letters are used for the name.

  16. ***Important***When writing arc measure an “m” must be used.Example: m AC = 80°

  17. SemicircleAn arc whose measure equals 180.

  18. CircumferenceC = 2πr

  19. Arc LengthThe measure of the length of an arc.

  20. ***Important***When writing arc length no “m” is used.Example:PB = 3π

  21. Calculating Arc Length Arc Measure • Circumference 360

  22. Calculating Arc Length(which is the same as) Arc Measure • Circumference 360

  23. Calculating Arc Length(which is the same as) Arc Measure • Circumference 360 Arc Measure • 2 π r 360

  24. Calculating Arc Length1) Divide the arc measure by 360. P 90 360 4m 90° B J

  25. Calculating Arc Length2) Find the circumference. P 90 360 4m 90° C = 2πr C = ? B J

  26. Calculating Arc Length2) Find the circumference. P 90 360 4m 90° C = 2πr C = 8π B J

  27. Calculating Arc Length3) Multiply the two. P 90 360 4m 90° C = 2πr C = 8π B J 90 • 8π = 2π 360

  28. Calculating Arc Length PB = P 4m 90° B J 2π

  29. Is there a maximum arc length?

  30. Is there a maximum arc length?No, it is a distance.

  31. Is there a maximum arc measure?

  32. Is there a maximum arc measure?Yes, 360.

  33. Turn to page 654.9, 10, 33, 3411-18, 24-26, 29-32, 39-43, 485 Points: 100% Complete 4 Points: 80% Complete 3 Points: 60% Complete 2 Points: 40% Complete 1 Point: 20% Complete

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