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A regular 12-gon with center O is inscribed in a unit circle. Let A, B, C be three consecutive vertices of the 12-gon as shown below. Let M be the intersection of AC and BO. Find AM. 

 

https://latex.artofproblemsolving.com/6/1/4/614ebc8a82efdae874074045ee068bceec61b95a.png

 

 Jan 20, 2019
 #1
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because there are twelve sides, you get twelve secotrs with 30 degrees each.

 

this means triangle AMO is 30-60-90 with a hypoutenuse of 1.

 

this means AM is 1/2.

 

HOPE THIS HELPED!

 Jan 20, 2019
 #2
avatar+143 
+1

Thanks so much! Now I understand it!!

noobieatmath  Jan 20, 2019

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