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7.6: Circles and Arcs

7.6: Circles and Arcs. Objectives: To find the measures of arcs and central angles To find the circumference and arc length. Central Angles and Arcs. The measure of an arc (in degrees) is equal to the measure of the central angle that intersects that arc m CB = 54°

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7.6: Circles and Arcs

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  1. 7.6: Circles and Arcs Objectives: To find the measures of arcs and central angles To find the circumference and arc length

  2. Central Angles and Arcs The measure of an arc (in degrees) is equal to the measure of the central angle that intersects that arc m CB = 54° What is m BAC ? What is the measure of a semicircle? 54°

  3. Find the indicated measures Given: Circle E Find: a.) b.) m AB c.) d.) m BCA B A E 120° C D

  4. Inscribed Angles: • The vertex of the angle is ON the circle:

  5. Examples: 1. Find 2. Find m AB

  6. What are the measures of the central angles?

  7. The number pi: • An irrational number: non-repeating, non-terminating • It is the ratio of the circle’s circumference to its diameter • APPROXIMATE using 3.14, 22/7 or pi button on calculator • When asked to leave answer in terms of pi, LEAVE IN YOUR ANSWER. It is the exact value. No need to use pi button or 3.14, etc..

  8. Circumference • The distance around a circle CIRCUMFERENCE = or d = diameter, r = radius If given diameter, use the first formula, if given radius, use the second.

  9. Find the circumference. Leave your answer in terms of pi. 7.5 in. 300 yd

  10. The diameter of a bicycle wheel is 22 in. To the nearest whole number, how many revolutions does the wheel make if the bike travels 100 ft? Find the circumference: How far does one revolution travel? Convert to feet: Divide 100 ft by answer:

  11. Concentric Circles How much longer is the distance around the outer circle than the inner? 30 ft 6 ft

  12. ARC LENGTH: A fraction of the circle’s circumference If an arc measures 60⁰, what fraction of the circle would it be? THEOREM: Length of arc = measure of arc • circumference of circle 360

  13. A length AB = m AB • 360 r B

  14. Find the length of each arc: Leave your answer in terms of • AB 2. ADB B A 10 ft 18 cm 60⁰ 150⁰ A D B

  15. Arc Length vs. Arc Measure Arc Length: Arc Measure: • How long is the arc • Measured in ft, in, cm, etc.. • Fraction of the circumference • Often given in terms of pi • If you were to straighten out a circle, it would be a straight line. Arc length would be the length of a segment cut off that line • Measured in degrees • How many degrees does the arc take up on the circle • Same measure as the central angle.

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