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In the circle below, AB is parallel to CD, AD is a diameter of the circle, and AD = 36.What is the length of AB? Express your answer in terms of pi.

 

 Jun 23, 2018
 #1
avatar+98197 
+1

Since  AD  is a diameter, then ABD will form a right triangle with angle ABD  = 90°

 

So...angle ADB   = 40°

 

And we can find AB  as :

 

sin (40)  = AB  / 36

 

AB  = 36 * sin (40)  = 23.140353948732  ≈   7.3658 pi  units

 

 

cool cool cool

 Jun 24, 2018
 #2
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+1

Here is another method:
If we designate O as the center of the circle, then:
Line AO = BO =radius of the circle = 18
ABO is an isosceles triangle with angles =50, 50, 80
18/sin(50) =AB/sin(80), and:
AB =23.14035 =7.3658pi

 Jun 24, 2018
 #3
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It sure is 7.3658 pi units! cool

 Jun 24, 2018

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