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10.9 Circumference and Arc Lengths

Understand how to find arc lengths on a circle given its circumference and measure, and calculate the radius of a circle. Learn to apply the formulas for arc lengths and circumferences in different scenarios. Examples provided for clarity.

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10.9 Circumference and Arc Lengths

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  1. 10.9 Circumference and Arc Lengths

  2. The circumference of a circle is its perimeter. C = πd Leave answer in terms of π unless asked to approximate. Then use a calculator.

  3. Length of an arc. The length of an arc depends on the circumference of the circle and the measure of the arc. T98: The length of an arc is equal to the circumference of its circle times the fractional part of the circle determined by the arc.

  4. A Given: circle O, arc AB = 40º, radius = 3 Find the length of arc AB. B O 40 degree arc is 40/360 = 1/9 of the circle Length of arc AB = 1/9 Circumference 1/9 (6π ) = 2/3π Remember: Length of arc = (m arc)πd 360 OR arc length= arc measure circumference 360

  5. 1. Given: Circle O’s circumference is 64π inches Find the radius of circle O O C = π d 64π = π d 64 = d 32 = radius 2. Find the length of the arc of a circle with a 12-cm radius and 105 arc.

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