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Ari draws twelve circles of diameter 2 inches that all pass through the same point, so that the angles formed by the diameters of any two consecutive circles are congruent, as in the image shown. What is the distance between point A and point B in inches? I notice that there are 30-60-90 triangles that may be formed here, but not sure where the right path is after that.  picture provided
 

 Mar 13, 2023
 #1
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I've seen this problem before. Stop cheating on your homework.

 Mar 13, 2023
 #2
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I'm not trying to cheat on any homework, I wanted to get more insight on how to solve this problem to learn how to use this on other problems

idontknowhowtodivide  Mar 13, 2023
 #3
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of course  of course!!!

Guest Mar 13, 2023
 #4
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By the law of cosines, AB = 3*sqrt(2) - 1.

 Mar 14, 2023
 #5
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Here is the pic, the answer is an approximation, you shouod be expected to work out the exact value.

 

I started with the 2 orange circles then rotate them about X by 360/12 = 30 degrees

You can see that point A is halfway between C and C'

 

Find the length of AX using cosine rule and then double it for  AB

 

 

 

 

 

 

 Mar 14, 2023
 #7
avatar+185 
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Thanks, just solved it on my own

idontknowhowtodivide  Mar 15, 2023

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