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Warm Up

Warm Up. Find the measure of each arc. JK JL JML JMK. M. N. 68°. 41°. L. J. K. 11.4 Circumference and Arc Length. Geometry. Circumference. The circumference of a circle is the distance around the circle. Theorem 11.6 Circumference of a Circle.

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Warm Up

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  1. Warm Up Find the measure of each arc. • JK • JL • JML • JMK M N 68° 41° L J K

  2. 11.4 Circumference and Arc Length Geometry

  3. Circumference The circumference of a circle is the distance around the circle.

  4. Theorem 11.6Circumference of a Circle The circumference C of a circle is C = πd or C = 2πr, where d is the diameter and r is the radius of the circle.

  5. Example Solve for a stool with a circular seat. • Find the circumference of a seat with a radius of 9in. • Find the radius of the seat with a circumference of 52in.

  6. Arc Length An arc length is a portion of a circumference of a circle. You can use the measure of the arc (in degrees) to find its length (in linear units).

  7. ARC LENGTH COROLLARY

  8. Example Find the length of arc JK. M 60° 16 in. J K

  9. Example Find the length of arc LM. L M 120° 8 in. K

  10. Example Find the length of arc RS. R 7 cm Q 45° S

  11. Shortcuts The length of a semicircle is one half the circumference, and the length of a 90 degree arc is one quarter of the cirumference

  12. Example Find the length of arc DG. D G 14 in. O

  13. Example Diameter BC is 17 in. long. Find the length of arc BDC. B D A C

  14. Example Find the length of arc AMT. A T 34 mm H M

  15. Using Arc Lengths

  16. Using Arc Lengths Find the mTUV if the arc length of TUV is 27 ft. U T S 6.3 ft V

  17. Using Arc Lengths Find the length of the radius. B 7.64 m A 60° C

  18. Using Arc Lengths Find the indicated measure. a) mLM b) circumference 16.76 in. R M L 10.2 cm Q 45° 8 in. K S

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