Find the measure of each arc.

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11.4 Circumference and Arc Length

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

Circumference and Arc Length Geometry

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

Theorem Circumference 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.

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.

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).

ARC LENGTH COROLLARY

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

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

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

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

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

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

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

Using Arc Lengths

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

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

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