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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!

AnonymousConfusedGuy  Apr 25, 2018
 #1
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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

Guest Apr 25, 2018
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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  !!!!

 

 

cool cool cool

CPhill  Apr 25, 2018
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Thanks you guys!

AnonymousConfusedGuy  Apr 25, 2018

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