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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?

 

 Dec 2, 2020
 #1
avatar+114592 
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From the center of the  circle (call it O )  connect    OB

 

Then  OB  = OA  = 18

So angle BAO  =angle ABO   = 42°

Then angle AOB =  180  - 2(42)  = 180 - 84 =  96°  

 

Using the Law of Cosines

 

AB^2 = (OA)^2  + (OB)^2   -2 (OA * OB) cos (AOB)

 

AB^2  =  (18)^2  + (18)^2  - 2(18*18) cos (96)

 

AB  = sqrt [  (18)^2  + (18)^2  - 2(18*18) cos (96) ]

 

AB = sqrt (715.7)  ≈   26.75

 

 

cool cool cool

 Dec 2, 2020
 #2
avatar+902 
0

AB = cos(42º) * AD

 Dec 2, 2020

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