Circumference

In a given circle a central angle of 40° intercepts a chord of 6 cm. What is the circumference of the circle?


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∠B = ∠A = 70°.


By the Law of Sines, the radius is  6  =  x  →  x  =  6 sin 70° .
sin 40° sin 70° sin 40°

The circumference is 2pir, or  2pi · 6 sin 70°  =  12pi · sin 70°  ≈  12 (3.14)(.94)
sin 40° sin 40° .64
 ≈ 55.34 cm

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