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Let A, B, and C be points on a circle of radius 18. If angle ACB = 70 degrees, what is the circumference of the minor arc {AB}?

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Let A, B, and C be points on a circle of radius 18. If angle ACB = 70 degrees, what is the circumference of the minor arc {AB}? Express your answer in terms of pi.

Thanks!

Apr 25, 2018

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I will take a crack at this! CPhill: Please check this. Thanks.

Let us designate the center of the circle as D

If the angle ACB was subteteded to the center of the circle D, then the formed angle ADB = 2 x angle ACB(70) = 140 degrees.

Will convert 140 degrees to radians =140Pi / 180 =7Pi/9, then the length of the arc AB=Angle ADB x Radius =7Pi/9 x 18 = 14Pi

Apr 25, 2018
#2
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ACB will be an inscribed angle......it it measures 70°, then the arc it intercepts (AB) has twice this measure = 140°

Then....the length of this minor arc is given by :

Arc Length  =  2 * pi * radius * (140 /360)  =

2 * pi * 18 *  ( 7/18)  =

2 * pi * 7   =

14 pi   units

Good Job, Guest  !!!!   Apr 25, 2018
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Thanks you guys!

Apr 25, 2018