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Hi!! I am having a little trouble with the following question. Could someone help me out? 

 

\(ABCDEFGHI\) is a regular nonagon with side length \(1\). Let \(M\) be the midpoint of \(\overline{EF}\). \(J\) is a point outside the nonagon such that \(AJ=2\) and \(\overline{AJ} \perp \overline{AM}\). Find all possible values of the product 
\[AJ\cdot BJ\cdot CJ\cdot DJ\cdot EJ\cdot FJ\cdot GJ\cdot HJ\cdot IJ\]
 

Thanks!

 Jan 3, 2024
 #1
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Turns out there was an error in the question, the nonagon should be inscribed in a circle of radius 1 instead of having a side length of 1. I'm still not sure how to solve it though.

 Jan 3, 2024
 #2
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Turns out there was an error in the question, the nonagon should be inscribed in a circle of radius 1 instead of having a side length of 1. Also, AJ=1.  I'm still not sure how to solve it though.

 Jan 3, 2024
edited by ElemetraryQuestions  Jan 3, 2024
edited by ElemetraryQuestions  Jan 3, 2024
 #3
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Unfortunately, your 'elemetary' question is a little too difficult for regular homework helpers. However, the answer is \(\sqrt{481}\) if CPhill is interested...

 Jan 3, 2024
edited by Holtran  Jan 3, 2024

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