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Let A, B, and C be points on a circle of radius 18. If angle ACB = 170 degrees, what is the circumference of the minor arc {AB}? Express your answer in terms of pi.

 Nov 26, 2020
 #1
avatar+419 
+1

Inscribed arc = 1/2 * arc measure

 

170 * 2 = 340

 

340/360 = 34/36 = 17/18 of the whole circle --> 18^2 * 17/18 * pi = 17*18 = 306 pi

 Nov 26, 2020
 #2
avatar+1039 
+3

170º * 2 = 340º    This is a major arc.

 

Minor arc is         360º - 340º = 20º

 

Minor arc {AB} = (36pi/360)*20 = 2pi

 

btw, major arc = 34pi

jugoslav  Nov 27, 2020
edited by Guest  Nov 27, 2020
 #4
avatar+419 
0

Oops... sorry, I meant to say that the minor arc must have 360-340 =20 degrees of measure, so it is 1/18 * 2 * 18 * pi = 2pi

 

Somehow I found the wrong area using the diameter ^^

Pangolin14  Nov 30, 2020
 #3
avatar+116126 
+1

Measure of major arc AB =  2 * 170 = 340

 

Measure of minor arc AB  =360 - 240 =   20° =   pi/9   rads

 

Arc length of  minor arc AB  =   radius * (theta in rads )  =   18 pi/9  =  2 pi

 

 

cool cool cool

 Nov 27, 2020

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