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Circles

This guide explores the properties of circles, including definitions of key terms such as center, radius, chord, diameter, and central angle. It highlights the relationship between diameter and circumference, introducing the constant pi and its significance. With practical examples, such as calculating the circumference of circles of varying sizes (e.g., a silver dollar, compact disc, table top), learners will gain hands-on experience in geometry. Engage with exercises to find central angles and apply the 360-degree rule. Perfect for students and anyone looking to deepen their understanding of circular geometry!

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Circles

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  1. Circles 9.6

  2. Circle - The set of infinite points equidistant from a center point. C - Center A X - Radius - Segment or distance from center to circle. O - Chord - Segment that connects one point on circle to another. Y - Diameter - Chord that passes through the center. M - Angle whose vertex is the center. - Central Angle

  3. 2(radius) = Diameter2r=d

  4. Circumference of a circle is the outside perimeter

  5. Circumference formulas

  6. What is Pi ( ) ?

  7. March 14

  8. Ratio of C:d Relationship Between Diameter and Circumference - Two easiest things to measure on a circle. Silver Dollar diameter Circumference 12.0 3.8 cm 12.0 cm 3.82 Compact Disc 37.7 12.0 cm 37.7 cm 12.0 Table Top 628.3 200 cm 628.3 cm 200

  9. Ratio of C:d 12.0 3.82 37.7 12.0 C d 628.3 200 Relationship Between Diameter and Circumference Silver Dollar Regardless of the size of the circle, the ratio of the circumference to the diameter remains constant. Compact Disc C d Table Top

  10. Circumference of a Circle C (d) (d) d Find the circumference of a circle with a diameter of 7 inches.

  11. Find the missing information. radius diameter Circumference 5 in. d = 2r 10 in. 4 m 8 m

  12. Making Circle Graphs • Central Angle- an angle whose vertex is in the center of the circle • There are 360 degrees in a circle • Use proportions to find the degree of each central angle

  13. Example: Find the measure of the central Angles • Swimming • Soccer

  14. Your turnFind the Central Angle of … • Track • Tennis

  15. Homework Page 472 (1-18) all • You may use a calculator but you need to still show work • Use 3.14 for pi • Round to three decimal places if need be

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